{"id":2286,"date":"2022-04-27T09:18:13","date_gmt":"2022-04-27T09:18:13","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2286"},"modified":"2024-03-15T06:44:10","modified_gmt":"2024-03-15T06:44:10","slug":"least-common-multiple-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple","title":{"rendered":"Least Common Multiple &#8211; Definition, Method, Solved Examples"},"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-df0740c4-54bd-49df-b9ba-aac9b505db77\" 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\/number-sense\/least-common-multiple#0-what-is-least-common-multiple-lcm>What Is Least Common Multiple (LCM)?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple#1-how-to-find-least-common-multiple-lcm>How to Find Least Common Multiple (LCM)?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple#2-listing-the-multiples-method>Listing the Multiples Method<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple#6-solved-examples-on-least-common-multiple>Solved Examples On Least Common Multiple<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple#7-practice-problems-on-least-common-multiple>Practice Problems On Least Common Multiple<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple#8-frequently-asked-questions-on-least-common-multiple>Frequently Asked Questions On Least Common Multiple<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<p class=\"eplus-wrapper\">A multiple is the product result of one number multiplied by another number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>For example,<\/strong> we can get the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiple\" target=\"_blank\" rel=\"noopener\" title=\"\">multiples<\/a> of 5 by multiplying 5 with numbers 1, 2, 3, and so on.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiples of 5 are: 5, 10, 15, 20, 25&#8230;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If a number is a multiple of two or more numbers, it is called a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/common-multiple\" target=\"_blank\" rel=\"noopener\" title=\"\">common multiple<\/a>. For example, 2 x 5 = 10.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, 10 is a multiple of both 2 and 5. Thus, 10 is said to be a common multiple of both 2 and 5.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-least-common-multiple-lcm\">What Is Least Common Multiple (LCM)?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>LCM is the short form for \u201cLeast Common Multiple.\u201d The least common multiple is defined as the smallest multiple that two or more numbers have in common.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example: Take two integers, 2 and 3.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiples of 2: 2, 4, <strong>6<\/strong>, 8, 10, <strong>12<\/strong>, 14, 16, <strong>18<\/strong>, 20\u2026.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiples of 3: 3, <strong>6<\/strong>, 9, <strong>12<\/strong>, 15, <strong>18<\/strong>, 21, 24, 27, 30 \u2026.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">6, 12, and 18 are common multiples of 2 and 3. The number 6 is the smallest. Therefore, 6 is the least common multiple of 2 and 3.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, what is LCM in math? The LCM of two numbers is the smallest number divisible by both numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">One prime application of LCM is finding the lowest common denominator (LCD) of two or more fractions. It plays a significant role in adding, subtracting, and comparing two or more fractions.<\/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\/10-and-100-more-than-the-same-number\" 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\/add_sub_pv_1_10_100_more_same_num_pt.png\" alt=\"10 and 100 More than the Same Number 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\">10 and 100 More than the Same Number 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\/add-1-digit-numbers\" 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\/add_sub_facts_add_make_10_pt.png\" alt=\"Add 1-Digit Numbers 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\">Add 1-Digit Numbers 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 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src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-Digit Numbers 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\">Add 2-Digit and 1-Digit Numbers 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\/add-2-digit-numbers-by-regrouping\" 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\/add_sub_pv_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping 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\">Add 2-Digit Numbers By Regrouping 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\/add-3-numbers\" 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\/add_sub_facts_add_3_no_pt.png\" alt=\"Add 3 Numbers 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\">Add 3 Numbers 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\/add-3-numbers-in-any-order\" 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\/add_sub_facts_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order 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\">Add 3 Numbers in Any Order 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 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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\/add_sub_facts_add_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model 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\">Add 3 Numbers using Model 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 = 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-how-to-find-least-common-multiple-lcm\">How to Find Least Common Multiple (LCM)?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Different methods to determine the LCM of a set of numbers are:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Listing the multiples<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Prime Factorization<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Division Method<br><\/li>\n<\/ul>\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\/10-and-100-more-than-a-3-digit-number\" 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\/10-and-100-more-than-a-3-digit-number.jpeg\" alt=\"10 and 100 More than a 3-digit Number\">\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\/100-more-and-100-less-than-a-3-digit-number\" 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\/100-more-and-100-less-than-a-3-digit-number.jpeg\" alt=\"100 More and 100 Less than a 3-digit Number\">\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\/100-more-than-a-3-digit-number\" 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\/100-more-than-a-3-digit-number.jpeg\" alt=\"100 More than a 3-digit Number\">\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\/add-subtract-multiples-of-10\" 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\/add-subtract-multiples-of-10.jpeg\" alt=\"Add & Subtract Multiples of 10 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\/add-subtract-ones-2-digit-numbers\" 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\" 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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\/add-1-digit-and-3-digit-numbers-and-match-the-sum\" 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\/add-1-digit-and-3-digit-numbers-and-match-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Match the Sum\">\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\/add-1-digit-and-3-digit-numbers-using-addition-tables\" 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\/add-1-digit-and-3-digit-numbers-using-addition-tables.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Tables\">\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\/add-1-digit-and-3-digit-numbers-using-addition-wheel\" 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\" 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class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-listing-the-multiples-method\">Listing the Multiples Method<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">To find the LCM using multiples, list the multiples of the numbers in the table as shown. The least common multiple is the first common multiple for the given numbers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"348\" height=\"79\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/multiples-of-12-and-16.png\" alt=\"Multiples of 12 and 16\" class=\"wp-image-40996\" title=\"Multiples of 12 and 16\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/multiples-of-12-and-16.png 348w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/multiples-of-12-and-16-300x68.png 300w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">For 12 and 16, the number 48 is the LCM.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-prime-factorization-method\">Prime Factorization Method<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The prime factorization method involves finding the prime factors of the given numbers and identifying the least common multiple (LCM). For example, pair the common multiples shown to find the least common multiple of 12 and 16 using the prime factorization. List them along with the remaining multiples.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/prime-factorization-of-12-and-16.png\" alt=\"Prime Factorization of 12 and 16\" class=\"wp-image-40997\" title=\"Prime Factorization of 12 and 16\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/prime-factorization-of-12-and-16.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/prime-factorization-of-12-and-16-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">LCM = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3 = 48<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-division-method\">Division Method<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this method, the given numbers are divided by the common <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/divisor\" target=\"_blank\" rel=\"noopener\" title=\"\">divisors<\/a> until there is no possible further division by the same number. The divisors and the remainders are multiplied to obtain the least common multiple.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example,&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"347\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/lcm-by-division-method.png\" alt=\"LCM by division method\" class=\"wp-image-40998\" title=\"LCM by division method\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/lcm-by-division-method.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/lcm-by-division-method-300x168.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">LCM =&nbsp; 2 \u00d7 2 \u00d7 3 \u00d7 4 = 48<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-relation-between-lcm-and-hcf\">Relation Between LCM and HCF<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The highest common factor of two or more numbers is the HCF of the given numbers. The smallest number among all common multiples of the given numbers is the least common multiple of two or more numbers. Assuming a and b are two numbers, the formula for determining the relationship between their LCM and HCF is:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>LCM (a, b) \u00d7 HCF (a, b) = a \u00d7 b<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-on-least-common-multiple\">Solved Examples On Least Common Multiple<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Find the LCM of 18 and 24 using the prime factorization method.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"266\" height=\"102\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/prime-factorization-of-18-and-24.png\" alt=\"Prime factorization of 18 and 24\" class=\"wp-image-40999\" title=\"Prime factorization of 18 and 24\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">LCM = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3 = 72<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: Find the smallest number divisible by 9 and 15.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The smallest number divisible by 9 and 15 is the LCM of 9 and 15.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"142\" height=\"107\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/prime-factorization-of-9-and-15.png\" alt=\"Prime factorization of 9 and 15\" class=\"wp-image-41000\" title=\"Prime factorization of 9 and 15\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">LCM = 3 \u00d7 3 \u00d7 5 = 45<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, 45 is the smallest number divisible by both 9 and 15.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: The product of the two numbers is 180. If their HCF is 3, what is their LCM?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The highest common factor (HCF) is 3, and the product of the numbers is 180.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since, LCM \u00d7 HCF = product of numbers, LCM = 1803 = 60<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the LCM is 60.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-least-common-multiple\">Practice Problems On Least Common Multiple<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Least Common Multiple - Definition With Examples<\/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\">The LCM of the two numbers is 12. Which of the following could be the other number if one of the numbers is 3?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">12<\/div><div class=\"spq_answer_block\" data-value=\"1\">8<\/div><div class=\"spq_answer_block\" data-value=\"2\">9<\/div><div class=\"spq_answer_block\" data-value=\"3\">11<\/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: 12<br\/>The LCM of a number and any of its multiples is the multiple itself.\r\n<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The LCM of two prime numbers is 91. What could the other number be if one of the numbers is 7?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">9<\/div><div class=\"spq_answer_block\" data-value=\"1\">11<\/div><div class=\"spq_answer_block\" data-value=\"2\">13<\/div><div class=\"spq_answer_block\" data-value=\"3\">19<\/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: 13<br\/>The LCM of two prime numbers is the product of the numbers. Since 7a = 91, a = 91\/7 = 13<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The HCF of two numbers, A and B, is 1. Which of the following is the LCM of A and B?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A \u00d7 B<\/div><div class=\"spq_answer_block\" data-value=\"1\">A \u00f7 B<\/div><div class=\"spq_answer_block\" data-value=\"2\">A + B<\/div><div class=\"spq_answer_block\" data-value=\"3\">A - B<\/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: A \u00d7 B<br\/>LCM \u00d7 HCF = product of numbers<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following is the LCM of 20 and 60?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">50<\/div><div class=\"spq_answer_block\" data-value=\"1\">30<\/div><div class=\"spq_answer_block\" data-value=\"2\">15<\/div><div class=\"spq_answer_block\" data-value=\"3\">60<\/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: 60<br\/>LCM of 20 and 60 = 60<\/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 Multiple - Definition With Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Least Common Multiple\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The LCM of the two numbers is 12. 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20 and 60 = 60\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCM of 20 and 60 = 60\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCM of 20 and 60 = 60\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCM of 20 and 60 = 60\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"60\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"LCM of 20 and 60 = 60\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"LCM of 20 and 60 = 60\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\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%\">\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%\">\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-least-common-multiple\">Frequently Asked Questions On Least Common Multiple<\/h2>\n<\/div>\n<\/div>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\" 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-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\"><strong><strong>How are the HCF and LCM of the two numbers related?<\/strong><\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap left\"><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-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\">\n\n<p class=\"eplus-wrapper\">The product of LCM and HCF of any given two numbers is equal to the product of those two 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-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\"><strong><strong>What is the difference between LCM and HCF?<\/strong><\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap left\"><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-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\">\n\n<p class=\"eplus-wrapper\">The LCM (Lowest Common Multiple) of two or more numbers is the smallest number among all common multiples of the provided numbers. In contrast, the HCF (Highest Common Factor) is the highest number among all the common factors of the 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-2-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\"><strong><strong>Why is the LCM of two co-prime numbers always their product?<\/strong><\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap left\"><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-e9f47cb8-b2d8-45d6-84e9-a9c32e619087\">\n\n<p class=\"eplus-wrapper\">The only common factor between the two co-prime numbers is 1. So, the HCF of two coprime numbers is always 1. If a and b are two co-prime numbers, then by the relationship between LCM and HCF, we get&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">LCM (a, b) \u00d7 HCF (a, b) = a \u00d7 b<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since a and b are co-prime numbers, their HCF is always 1. So, we get that the LCM of a and b is always the product of a and b.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A multiple is the product result of one number multiplied by another number. For example, we can get the multiples of 5 by multiplying 5 with numbers 1, 2, 3, and so on. Multiples of 5 are: 5, 10, 15, 20, 25&#8230; If a number is a multiple of two or more numbers, it is &#8230; <a title=\"Least Common Multiple &#8211; Definition, Method, Solved Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple\" aria-label=\"More on Least Common Multiple &#8211; Definition, Method, Solved Examples\">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-2286","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\/2286","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=2286"}],"version-history":[{"count":17,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2286\/revisions"}],"predecessor-version":[{"id":41001,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2286\/revisions\/41001"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2286"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2286"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}