## Least Common Denominator

**Fractions**

Fractions are the numbers between two integers written in the form ofpq. We express these numbers in the form of a quotient or fraction of two integers.

In a fraction, the “p” is the numerator and “q” is the denominator. The value of “q” must be a non-zero integer. For a unit fraction, “p” is always equal to “1”.

To understand it better, let’s find the numbers on the number line as follows:

The number 0.8 lies between 0 and 1 and the number 2.5 lies between 2 and 3. We can also write them as:

0.8 = 810, which can be simplified as 45

2.5 = 2510 , which can be simplified as 102

The number 52 is an example of improper fraction where the numerator > denominator

Fractions 12 , 32 , 52 and 165 marked on a number line.

## Least Common Denominator

The least common denominator is the smallest number of all the common multiples of the denominators when 2 or more fractions are given. Let’s add two fractions.

= 29 + 34

Since adding them will be difficult as the denominators are not the same, thus we need to find a common number to simplify it. For this, list the multiples of the number 9 and 4 in a table. The first common smallest multiple will be the least common denominator for the given fractions.

Here, the least common multiple for 9 and 4 is 36. Thus, the expression can be written as:

= 29 + 34 = 29 x 44 + 34 x 99

= 836 + 2736

= 29 x 44 + 34 x 99

= 3536

## Ordering Fractions (Least to Greatest)

Using the least common denominator, fractions can be arranged in ascending or descending order.

For example, to arrange the following numbers in ascending order, we find their LCD.

35 , 920 , 46

Using the table of multiples above, the LCD will be 60. Thus numbers can be rewritten as:

3660 , 2760 , 4060

2760 < 3660 < 4060

## Application

The concept of least common denominator for fractions is useful to evaluate the result as a part of the whole. In creating a solution using chemicals, the measurements using a cup, tube or flask, etc. are marked with fractions to maintain precision. Several areas in chemical science, physics, currency exchange, computing interest, time duration, etc. use fractions to represent the values.

Fun Facts1. During 1800 BC, Egyptians used hieroglyphs (picture-based writing) of a mouth (represents a part) to represent unit fractions. 2. Romans used words to represent fractions with base 12, such as “Uncia” for 112, “Semis” for 612 , etc. |

**Related Math Vocabulary**

- Multiples and multiplication
- Least Common Multiple
- Number operations
- Fractions
- Number ordering

## Practice Problems

## Least Common Denominator## 1What is the least common denominator that can be used to compare the fractions 1/2, 2/3, 1/4?24 6 12 9 CorrectIncorrect Correct answer is: 12 The least common multiple of the denominators 2, 3, and 4 is 12. Therefore, LCD of the given fractions = 12. ## 2Find the least common denominator for the pair of fractions 1/5 and 4/10.10 4 5 15 CorrectIncorrect Correct answer is: 10 The least common multiple of the denominators 5 and 10 is 10. Therefore, LCD of the given fractions = 10. ## 3Find the least common denominator for the pair of fractions 1/7 and 5/8.15 56 8 7 CorrectIncorrect Correct answer is: 56 The least common multiple of the denominators 7 and 8 is 56. Therefore, LCD of the given fractions = 56. ## 4The fraction 45/10 lies between which two numbers?3 and 4 45 and 46 0 and 1 4 and 5 CorrectIncorrect Correct answer is: 4 and 5 45/10 = 4.5. So, 4.5 is a decimal number that lies between 4 and 5. |

## Frequently Asked Questions

**How do you find the least common denominator?**

First, take the two different denominators and start making multiples of each of them…one times the numbers, two times the numbers, three times the numbers, and so on. As soon as you find a multiple that is the same for both numbers, that is the least common multiple or the least common denominator.

**Are LCM and LCD the same or different?**

The mathematical approach to finding the LCM and LCD is the same. For both, we need to find the least common multiple of two or more numbers. The least common denominator (LCD) is actually the least common multiple (LCM) of the denominators.

**How are the LCD and GCF different?**

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.

**Why is finding the least common denominator important?**

Finding the least common denominator helps in adding and subtracting fractions when they don’t have the same denominator. It makes the calculations a lot easier. The LCD also helps when kids are working with rational expressions in higher grades.