{"id":2135,"date":"2022-04-26T09:14:54","date_gmt":"2022-04-26T09:14:54","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2135"},"modified":"2023-11-28T05:11:05","modified_gmt":"2023-11-28T05:11:05","slug":"area-of-a-quadrilateral-definition-with-examples-copy-2","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator","title":{"rendered":"Least Common Denominator &#8211; Definition, Examples, Facts, FAQs"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-1a96f954-159f-4ca1-a8b1-b3e14e2ec8a6\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator#0-what-is-the-least-common-denominator>What Is the Least Common Denominator?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator#2-how-to-find-the-least-common-denominator>How to Find the Least Common Denominator<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator#3-applications-of-least-common-denominator>Applications of Least Common Denominator<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator#7-solved-examples-on-least-common-denominator>Solved Examples on Least Common Denominator<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator#8-practice-problems-on-least-common-denominator>Practice Problems on Least Common Denominator<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator#9-frequently-asked-questions-on-least-common-denominator>Frequently Asked Questions on Least Common Denominator<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-least-common-denominator\">What Is the Least Common Denominator?<\/h2>\n\n\n\n<p><strong>The least common denominator (LCD) is the smallest number divisible by all denominators of the given set of fractions. It is the smallest number among the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/common-multiple\"><strong>common multiples<\/strong><\/a><strong> of the denominators.&nbsp;<\/strong><\/p>\n\n\n\n<p>In simple words, LCD is the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple\">LCM<\/a> of the denominators of the given fractions.<\/p>\n\n\n\n<p>The concept of LCD in math is really useful when it comes to comparing, adding or subtracting unlike fractions.<\/p>\n\n\n\n<p><strong>Example: <\/strong>Add the fractions $\\frac{1}{9}$ and $\\frac{3}{5}$.&nbsp;<\/p>\n\n\n\n<p>To add any two fractions, firstly we check if the denominators are the same.<\/p>\n\n\n\n<p>Here, the denominators are 9 and 5.&nbsp;&nbsp;<\/p>\n\n\n\n<p>Find the least common denominator.<\/p>\n\n\n\n<p><strong>Multiples of <\/strong>$9 = 9,\\; 18,\\; 27,\\; 36,\\; 45$, \u2026<\/p>\n\n\n\n<p><strong>Multiples of <\/strong>$5 = 5,\\; 10,\\; 15,\\; 20,\\; 25,\\; 30,\\; 35,\\; 40,\\; 45$, \u2026<\/p>\n\n\n\n<p><strong>Common multiples of 9 and <\/strong>$5 = 45,\\; 50,\\; 95$, \u2026<\/p>\n\n\n\n<p><strong>LCM (9, 5)<\/strong> $=$ LCD<strong> <\/strong>$(\\frac{1}{9}$ and $\\frac{3}{5})= 45$<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-greatest-or-least-decimal\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_make_way_24_gm.png\" alt=\"Choose Greatest or Least 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class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-missing-number-in-the-multiplication-solution\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_find_missing_2dby1d_pt.png\" alt=\"Choose the Missing Number in the Multiplication Solution Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Missing Number in the Multiplication Solution Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div 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class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_make_way_20_gm.png\" alt=\"Compare Fractions with Different Denominators Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare Fractions with Different Denominators Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-fractions-with-like-denominators\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_make_way_18_gm.png\" alt=\"Compare Fractions with Like Denominators Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare Fractions with Like Denominators Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n    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number of all the common multiples of denominators. <\/strong><strong>It is also known as the Lowest Common Denominator (abbreviated as LCD).<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expression-for-array\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expression-for-array.jpeg\" alt=\"Addition and Multiplication Expression for Array Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expressions.jpeg\" alt=\"Addition and Multiplication Expressions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-multiplication-in-everyday-life\" 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Multiplication Expressions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/comparing-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/comparing-multiplication-expressions.jpeg\" alt=\"Comparing Multiplication Expressions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/complete-multiplication-and-division-sentences\" 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});\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-how-to-find-the-least-common-denominator\">How to Find the Least Common Denominator<\/h2>\n\n\n\n<p>To find the least common denominator, we can use either of the ways as given below:&nbsp;<\/p>\n\n\n\n<p><strong>Listing Method<\/strong><\/p>\n\n\n\n<p>One way is to list the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiple\" title=\"\">multiples<\/a> of both the denominators. This method is convenient to use when the denominators are small numbers.<\/p>\n\n\n\n<p><strong>Example: Find the least common denominator of <\/strong>$\\frac{5}{8}$<strong> and <\/strong>$\\frac{11}{12}$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p>Multiples of $8 = 8,\\; 16,\\; 24,\\; 32,\\; 40,\\; 48$,&#8230;&nbsp;<\/p>\n\n\n\n<p>Multiples of $12 = 12,\\; 24,\\; 36,\\; 48$,\u2026&nbsp;<\/p>\n\n\n\n<p>Common Multiples of 8 and $12 = 24,\\; 48$,&#8230;<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p>LCD $(\\frac{5}{8} ,\\; \\frac{11}{12}) =$ LCM (8,12) $= 24$<\/p>\n\n\n\n<p>We can make the denominators of $\\frac{5}{8}$ and $\\frac{11}{12}$ same by finding the LCD. Multiply both numerator and denominator of $\\frac{5}{8}$ with 3. Multiply both numerator and denominator of $\\frac{11}{12}$ with 2.<\/p>\n\n\n\n<p>$\\frac{5}{8} \\times \\frac{3}{3}= \\frac{15}{24}$<\/p>\n\n\n\n<p>$\\frac{11}{12}\\times \\frac{2}{2} = \\frac{22}{24}$<\/p>\n\n\n\n<p><strong>Prime Factorization Method<\/strong><\/p>\n\n\n\n<p>Find the prime factorization of the denominators. Identify the common (matching) factors. Note down the remaining factors. Multiply them together.&nbsp;<\/p>\n\n\n\n<p><strong>Example:<\/strong> &nbsp;$\\frac{5}{21},\\; \\frac{3}{30}$<\/p>\n\n\n\n<p>Prime factorization of $21 = 3\\times7$<\/p>\n\n\n\n<p>Prime factorization of $30 = 3\\times2\\times5$<\/p>\n\n\n\n<p>Common factors $= 3$<\/p>\n\n\n\n<p>Uncommon factors $= 2,\\; 7,\\; 5$<\/p>\n\n\n\n<p>LCD $= 2 \\times7 \\times5 \\times3 = 210$<\/p>\n\n\n\n<p><strong>NOTE: If the two or more denominators have HCF <\/strong>$= 1$<strong>, simply multiply the denominators to find the LCD.&nbsp;<\/strong><\/p>\n\n\n\n<p>For example, $\\frac{1}{9}$ and $\\frac{4}{7}$.&nbsp;<\/p>\n\n\n\n<p>Since the HCF of 9 and 7 is 1, the Least Common Denominator is the product of two denominators. On multiplying the denominators, we get $9 \\times 7 = 63$.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-applications-of-least-common-denominator\">Applications of Least Common Denominator<\/h2>\n\n\n\n<p>The concept of LCD in math is really helpful when working with fractions. Let\u2019s see how to simplify operations on fractions using the least common denominator.<\/p>\n\n\n\n<p>We will discuss two points.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Comparing &amp; ordering fractions using the least common denominator<\/li>\n\n\n\n<li>Adding and subtracting fractions using the least common denominator<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-comparing-and-ordering-fractions-using-lcd\">Comparing and Ordering Fractions Using LCD<\/h2>\n\n\n\n<p>We can easily compare and order unlike fractions by finding LCD.<\/p>\n\n\n\n<p><strong>Example:<\/strong> Find the LCD of the fractions: $\\frac{3}{5},\\;\\frac{4}{6},\\;\\frac{9}{20}$<\/p>\n\n\n\n<!DOCTYPE html>\n<html>\n<head>\n  <style>\n   .custom-figure{\n   overflow-x: auto;\n}\n    table {\n      border-collapse: collapse;\n      width: 800px;\n    }\n    table td {\n      padding: 10px;\n      border: 1px solid black;\n      text-align: center;\n      width: auto;\n    }\n    \n    \/* Define the color pattern *\/\n    .custom-1 {\n      background-color: #ffe788;\n    }\n    \n    .custom-2 {\n      background-color: #c8daf9;\n    }\n  <\/style>\n<\/head>\n<figure class =\"custom-figure\">\n  <table class=\"wj-table-class\">\n    <tr>\n      <td class=\"custom-1\">5<\/td>\n      <td class=\"color-1\">5<\/td>\n      <td class=\"color-2\">10<\/td>\n      <td class=\"color-2\">15<\/td>\n      <td class=\"color-3\">20<\/td>\n      <td class=\"color-3\">25<\/td>\n      <td class=\"color-4\">30<\/td>\n      <td class=\"color-4\">35<\/td>\n      <td class=\"color-1\">40<\/td>\n      <td class=\"color-1\">45<\/td>\n      <td class=\"color-2\">50<\/td>\n      <td class=\"color-2\">55<\/td>\n      <td class=\"custom-2\">60<\/td>\n    <\/tr>\n    <tr>\n      <td class=\"custom-1\">6<\/td>\n      <td class=\"color-3\">6<\/td>\n      <td class=\"color-4\">12<\/td>\n      <td class=\"color-4\">18<\/td>\n      <td class=\"color-1\">24<\/td>\n      <td class=\"color-1\">30<\/td>\n      <td class=\"color-2\">36<\/td>\n      <td class=\"color-2\">42<\/td>\n      <td class=\"color-3\">48<\/td>\n      <td class=\"color-3\">54<\/td>\n      <td class=\"custom-2\">60<\/td>\n      <td class=\"color-4\">66<\/td>\n      <td class=\"color-1\">72<\/td>\n    <\/tr>\n    <tr>\n      <td class=\"custom-1\">20<\/td>\n      <td class=\"color-1\">20<\/td>\n      <td class=\"color-2\">40<\/td>\n      <td class=\"custom-2\">60<\/td>\n      <td class=\"color-3\">80<\/td>\n      <td class=\"color-3\">100<\/td>\n      <td class=\"color-4\">120<\/td>\n      <td class=\"color-4\">140<\/td>\n      <td class=\"color-1\">160<\/td>\n      <td class=\"color-1\">180<\/td>\n      <td class=\"color-2\">200<\/td>\n      <td class=\"color-2\">220<\/td>\n      <td class=\"color-3\">240<\/td>\n    <\/tr>\n  <\/table>\n<\/figure>\n<\/html>\n\n\n\n<p>Using the table of multiples above, we can observe that<\/p>\n\n\n\n<p>LCM of 5, 20 and $6 = 60$.<\/p>\n\n\n\n<p>Thus, LCD of the given fractions is 60&nbsp;<\/p>\n\n\n\n<p>The fractions can be rewritten as: $\\frac{36}{60},\\;\\frac{40}{60},\\;\\frac{27}{60}$<\/p>\n\n\n\n<p><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/ascending-order\" title=\"\">Ascending order<\/a>: $\\frac{27}{60}\\lt\\frac{36}{60}\\lt\\frac{40}{60} \\Rightarrow \\frac{9}{20}\\lt\\frac{3}{5}\\lt\\frac{4}{6}$<\/p>\n\n\n\n<p><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/descending-order\" title=\"\">Descending order<\/a>: $\\frac{40}{60}\\gt\\frac{36}{60}\\gt\\frac{27}{60} \\Rightarrow \\frac{4}{6}\\gt\\frac{3}{5}\\gt\\frac{9}{20}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-adding-and-subtracting-fractions-using-lcd\">Adding and Subtracting Fractions Using LCD<\/h2>\n\n\n\n<p>Using the least common denominator, fractions can be added and subtracted.<\/p>\n\n\n\n<p><strong>Example 1:<\/strong> Find: $\\frac{5}{6}\\;-\\;\\frac{9}{20}$.<\/p>\n\n\n\n<p>$6 = 2 \\times 3$<\/p>\n\n\n\n<p>$20 = 2 \\times 2 \\times 5$<\/p>\n\n\n\n<p>LCM (6, 20) $= 2 \\times2 \\times3 \\times5 = 60$<\/p>\n\n\n\n<p>LCD $(\\frac{5}{6},\\;\\frac{9}{20}) = 60$<\/p>\n\n\n\n<p>$\\frac{5\\times10}{6\\times10} = \\frac{50}{60}$<\/p>\n\n\n\n<p>$\\frac{9\\times3}{20\\times3} = \\frac{27}{60}$<\/p>\n\n\n\n<p>We get<\/p>\n\n\n\n<p>$\\frac{5}{6}\\;-\\;\\frac{9}{20} = \\frac{50}{60}\\;-\\;\\frac{27}{60} = \\frac{13}{60}$<\/p>\n\n\n\n<p><strong>Example 2: Find <\/strong>$\\frac{3}{4} + \\frac{1}{5}$.&nbsp;<\/p>\n\n\n\n<p>Since GCD$(4,\\; 5) = 1$, LCM $(4,\\; 5) = 4\\times 5 = &nbsp;20$<\/p>\n\n\n\n<p>LCD$(\\frac{3}{4},\\;\\frac{1}{5}) = 20$<\/p>\n\n\n\n<p>The fractions can be rewritten as $\\frac{15}{20}$ and $\\frac{4}{20}$.<\/p>\n\n\n\n<p>Sum $= \\frac{15}{20} + \\frac{4}{20} = \\frac{19}{20}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about Least Common Denominator, its definition, applications along with examples on how to find LCD. Let\u2019s solve a few more examples and practice problems for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-solved-examples-on-least-common-denominator\">Solved Examples on Least Common Denominator<\/h2>\n\n\n\n<p><strong>1. Find the LCD for <\/strong>$\\frac{2}{5},\\;\\frac{1}{7}$<strong> and <\/strong>$\\frac{4}{9}$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The denominators 5, 7, and 9 have no common factors other than 1.<\/p>\n\n\n\n<p>HCF (5, 7 and 9) $= 1$<\/p>\n\n\n\n<p>Thus, LCM (5, 7 and 9) $= 5 \\times 7 \\times 9 = 315$<\/p>\n\n\n\n<p>LCD$(\\frac{2}{5},\\;\\frac{1}{7},\\;\\frac{4}{9}) =&nbsp; 315$.<\/p>\n\n\n\n<p><strong>2. Simplify: <\/strong>$\\frac{21}{4}\\;-\\;\\frac{7}{3}$<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>We will first find the LCD of the denominators.<\/p>\n\n\n\n<p>LCM (3, 4) $= 12$<\/p>\n\n\n\n<p>LCD $(\\frac{21}{4},\\;\\frac{7}{3}) = 12$<\/p>\n\n\n\n<p>$\\frac{21\\times3}{4\\times3} = \\frac{63}{12}$ and $\\frac{7\\times4}{3\\times4} = \\frac{28}{12}$<\/p>\n\n\n\n<p>$\\frac{21}{4}\\;-\\;\\frac{7}{3} = \\frac{63}{12}\\;-\\;\\frac{28}{12} = \\frac{35}{12}$<\/p>\n\n\n\n<p><strong>3. Find the LCD of <\/strong>$\\frac{7}{8}$<strong> and <\/strong>$\\frac{1}{6}$<strong> by listing multiples.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Multiples of $8 = 8,\\; 16,\\; 24,\\; 32,\\; 40,\\; 48$, \u2026<\/p>\n\n\n\n<p>Multiples of $6 = 6,\\; 12,\\; 18,\\; 24,\\; 30,\\; 36$, \u2026<\/p>\n\n\n\n<p>LCM(8, 6) $= 24$<\/p>\n\n\n\n<p>Thus, LCD$(\\frac{7}{8},\\; \\frac{1}{6}) = 24$<\/p>\n\n\n\n<p><strong>4. Compare the fractions <\/strong>$\\frac{2}{9},\\;\\frac{3}{4}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>9 and 4 have no common factor other&nbsp; than 1.<\/p>\n\n\n\n<p>Thus, LCM(4, 9) $= 9\\times4 = 36$<\/p>\n\n\n\n<p>Thus, LCD$(\\frac{7}{8}$ and $\\frac{1}{6}) = 36$<\/p>\n\n\n\n<p>Let\u2019s rewrite the fractions using the common denominator.<\/p>\n\n\n\n<p>$\\frac{2}{9} = \\frac{8}{36}$ and $\\frac{3}{4} = \\frac{27}{36}$<\/p>\n\n\n\n<p>Here, $\\frac{8}{36} \\lt \\frac{27}{36}$<\/p>\n\n\n\n<p>Thus, $\\frac{2}{9} \\lt \\frac{3}{4}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-practice-problems-on-least-common-denominator\">Practice Problems on Least Common Denominator<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Least Common Denominator<\/h2><p style=\"display:none;\">Attend this Quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following holds true?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{6}\\lt\\frac{5}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{2}{7}\\lt\\frac{1}{11}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{2}{3}\\lt\\frac{8}{13}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{10}\\gt\\frac{7}{8}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{1}{6}\\lt\\frac{5}{8}$<br\/>LCD $=$ LCM $(6,\\; 8) = 24$<br>\r\n$\\frac{1\\times4}{6\\times4} = \\frac{4}{24}$ and $\\frac{5\\times3}{8\\times3} = \\frac{15}{24}$<br>\r\n$\\frac{4}{24}\\lt\\frac{15}{24}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The Least Common Denominator of fractions is simply the ____ of all denominators.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">GCF<\/div><div class=\"spq_answer_block\" data-value=\"1\">HCF<\/div><div class=\"spq_answer_block\" data-value=\"2\">GCD<\/div><div class=\"spq_answer_block\" data-value=\"3\">LCM<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: LCM<br\/>The LCD of fractions is calculated by finding the LCM of the denominators.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The LCD of $\\frac{1}{3}$ and $\\frac{1}{4}$ is ____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{12}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{7}{12}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{5}{12}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{11}{12}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{5}{12}$<br\/>3 and 4 are coprimes. So, HCF$(3,\\; 4) = 1$<br>\r\nLCM $(3,\\; 4) = 12$<br>\r\nThus, LCD of $\\frac{1}{3}$ and $\\frac{1}{4}$ is $3\\times4 = 12$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The LCD is the smallest number that is _____ all denominators.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">divisible by<\/div><div class=\"spq_answer_block\" data-value=\"1\">a factor of<\/div><div class=\"spq_answer_block\" data-value=\"2\">a divisor of<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: divisible by<br\/>Since the LCD is a LCM of denominators. Thus, it is basically a multiple of denominators. Thus, it is divisible by all denominators.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this Quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Least Common Denominator\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Least Common Denominator\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following holds true?\",\n                    \"text\": \"Which of the following holds true?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"LCD $$=$$ LCM $$(6,\\\\; 8) = 24$$<br>\r\n$$\\\\frac{1\\\\times4}{6\\\\times4} = \\\\frac{4}{24}$$ and $$\\\\frac{5\\\\times3}{8\\\\times3} = \\\\frac{15}{24}$$<br>\r\n$$\\\\frac{4}{24}\\\\lt\\\\frac{15}{24}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{7}\\\\lt\\\\frac{1}{11}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCD $$=$$ LCM $$(6,\\\\; 8) = 24$$<br>\r\n$$\\\\frac{1\\\\times4}{6\\\\times4} = \\\\frac{4}{24}$$ and $$\\\\frac{5\\\\times3}{8\\\\times3} = \\\\frac{15}{24}$$<br>\r\n$$\\\\frac{4}{24}\\\\lt\\\\frac{15}{24}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{3}\\\\lt\\\\frac{8}{13}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCD $$=$$ LCM $$(6,\\\\; 8) = 24$$<br>\r\n$$\\\\frac{1\\\\times4}{6\\\\times4} = \\\\frac{4}{24}$$ and $$\\\\frac{5\\\\times3}{8\\\\times3} = \\\\frac{15}{24}$$<br>\r\n$$\\\\frac{4}{24}\\\\lt\\\\frac{15}{24}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{10}\\\\gt\\\\frac{7}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCD $$=$$ LCM $$(6,\\\\; 8) = 24$$<br>\r\n$$\\\\frac{1\\\\times4}{6\\\\times4} = \\\\frac{4}{24}$$ and $$\\\\frac{5\\\\times3}{8\\\\times3} = \\\\frac{15}{24}$$<br>\r\n$$\\\\frac{4}{24}\\\\lt\\\\frac{15}{24}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{6}\\\\lt\\\\frac{5}{8}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"LCD $$=$$ LCM $$(6,\\\\; 8) = 24$$<br>\r\n$$\\\\frac{1\\\\times4}{6\\\\times4} = \\\\frac{4}{24}$$ and $$\\\\frac{5\\\\times3}{8\\\\times3} = \\\\frac{15}{24}$$<br>\r\n$$\\\\frac{4}{24}\\\\lt\\\\frac{15}{24}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"LCD $$=$$ LCM $$(6,\\\\; 8) = 24$$<br>\r\n$$\\\\frac{1\\\\times4}{6\\\\times4} = \\\\frac{4}{24}$$ and $$\\\\frac{5\\\\times3}{8\\\\times3} = \\\\frac{15}{24}$$<br>\r\n$$\\\\frac{4}{24}\\\\lt\\\\frac{15}{24}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The Least Common Denominator of fractions is simply the ____ of all denominators.\",\n                    \"text\": \"The Least Common Denominator of fractions is simply the ____ of all denominators.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The LCD of fractions is calculated by finding the LCM of the denominators.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"GCF\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The LCD of fractions is calculated by finding the LCM of the denominators.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"HCF\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The LCD of fractions is calculated by finding the LCM of the denominators.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"GCD\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The LCD of fractions is calculated by finding the LCM of the denominators.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"LCM\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The LCD of fractions is calculated by finding the LCM of the denominators.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The LCD of fractions is calculated by finding the LCM of the denominators.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is ____.\",\n                    \"text\": \"The LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is ____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"3 and 4 are coprimes. So, HCF$$(3,\\\\; 4) = 1$$<br>\r\nLCM $$(3,\\\\; 4) = 12$$<br>\r\nThus, LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is $$3\\\\times4 = 12$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{12}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"3 and 4 are coprimes. So, HCF$$(3,\\\\; 4) = 1$$<br>\r\nLCM $$(3,\\\\; 4) = 12$$<br>\r\nThus, LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is $$3\\\\times4 = 12$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{7}{12}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"3 and 4 are coprimes. So, HCF$$(3,\\\\; 4) = 1$$<br>\r\nLCM $$(3,\\\\; 4) = 12$$<br>\r\nThus, LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is $$3\\\\times4 = 12$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{11}{12}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"3 and 4 are coprimes. So, HCF$$(3,\\\\; 4) = 1$$<br>\r\nLCM $$(3,\\\\; 4) = 12$$<br>\r\nThus, LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is $$3\\\\times4 = 12$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{5}{12}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"3 and 4 are coprimes. So, HCF$$(3,\\\\; 4) = 1$$<br>\r\nLCM $$(3,\\\\; 4) = 12$$<br>\r\nThus, LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is $$3\\\\times4 = 12$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"3 and 4 are coprimes. So, HCF$$(3,\\\\; 4) = 1$$<br>\r\nLCM $$(3,\\\\; 4) = 12$$<br>\r\nThus, LCD of $$\\\\frac{1}{3}$$ and $$\\\\frac{1}{4}$$ is $$3\\\\times4 = 12$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The LCD is the smallest number that is _____ all denominators.\",\n                    \"text\": \"The LCD is the smallest number that is _____ all denominators.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Since the LCD is a LCM of denominators. Thus, it is basically a multiple of denominators. Thus, it is divisible by all denominators.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a factor of\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since the LCD is a LCM of denominators. Thus, it is basically a multiple of denominators. Thus, it is divisible by all denominators.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"a divisor of\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since the LCD is a LCM of denominators. Thus, it is basically a multiple of denominators. Thus, it is divisible by all denominators.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since the LCD is a LCM of denominators. Thus, it is basically a multiple of denominators. Thus, it is divisible by all denominators.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"divisible by\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Since the LCD is a LCM of denominators. Thus, it is basically a multiple of denominators. Thus, it is divisible by all denominators.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Since the LCD is a LCM of denominators. Thus, it is basically a multiple of denominators. Thus, it is divisible by all denominators.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-frequently-asked-questions-on-least-common-denominator\">Frequently Asked Questions on Least Common Denominator<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\"><strong>What is the difference between LCM and LCD? Are LCM and LCD the same or different?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\">\n\n<p>LCD of fractions is the LCM of the denominators of the fractions. LCM of two or more numbers is the smallest number of common multiples of given numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\"><strong>How is LCD different from the common denominator?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\">\n\n<p>Least Common Denominator is the smallest common multiple of the common multiples of the denominators of a set of fractions. On the other hand, the common denominator is the common multiple of the denominators. For example: For the fractions $\\frac{3}{5}$ and $\\frac{2}{7}$, the least common denominator is 35. The common denominator can be 35, 70, 105, etc.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\"><strong>How are the LCD and GCF different?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\">\n\n<p>LCD stands for Least Common Denominator and GCF stands for Greatest Common Factor. They are just about opposites. LCD is the least multiple that is the same for two or more denominators whereas, the GCF of two or more numbers is the greatest factor that these numbers share.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\"><strong>Can you find the LCD by simply multiplying the denominators?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-53aa6cd8-d8ef-4f9f-8882-06fc3460bf43\">\n\n<p>Multiplying all of the denominators results in a common denominator between the fractions, it does not always give you the LCD. If the GCF of denominators is 1, then the LCD of fractions can be calculated by simply multiplying the denominators.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is the Least Common Denominator? The least common denominator (LCD) is the smallest number divisible by all denominators of the given set of fractions. It is the smallest number among the common multiples of the denominators.&nbsp; In simple words, LCD is the LCM of the denominators of the given fractions. The concept of LCD &#8230; <a title=\"Least Common Denominator &#8211; Definition, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/least-common-denominator\" aria-label=\"More on Least Common Denominator &#8211; Definition, Examples, Facts, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-2135","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=2135"}],"version-history":[{"count":59,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2135\/revisions"}],"predecessor-version":[{"id":36286,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2135\/revisions\/36286"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}