LCD - Least Common Denominator - Definitions, Methods, Examples

Least Common Denominator - LCD

When two or more fractions have the same denominators, they are termed as the common denominators. The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions. For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators. In this lesson, we will learn how to find the least common denominator in detail.

1.	What is Least Common Denominator?
2.	How to Find the Least Common Denominator?
3.	Solved Examples on Least Common Denominator
4.	Practice Questions on Least Common Denominator
5.	FAQs on Least Common Denominator

What is Least Common Denominator?

The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given. 

Let’s add the fractions: (2/9)+(3/4)

For adding any two fractions, we first check if the denominators are the same or not as we can add or subtract only like fractions. Since the denominators are 9 and 4, we need to find a common number that is a multiple of both. This common multiple will help us simplify the problem. Thus, the least common multiple obtained for 9 and 4 is 36. Therefore, the expression can be written as:

(2/9)+(3/4) = (2/9 × 4/4) + (3/4 × 9/9) = (8/36) + (27/36) = 35/36

How to Find the Least Common Denominator?

In order to find the least common denominator, we can opt for either of the ways as given below:

• List the multiples of both denominators. For example, 2/15 and 1/25. The multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, ... and the multiples of 25 are 25, 50, 75, 100, 125, 150, 175, 200, 225, 250. Thus, the least common denominator will be 150 and the fractions will be 20/150 and 6/150 (by taking LCM)
• Multiply both the denominators. For example, 3/4 and 2/7. Here, the two denominators, 4 and 7 don't have any common multiple as such. Thus, we will multiply both the denominators. Thus, the least common denominator will be 28 and the fractions will be 21/28 and 8/28.

Apart from simplifying fractions, the least common denominator can be used to arrange fractions in ascending or descending order. For example, we can arrange the following fractions in ascending order by finding their LCD: (3/5, 9/20, 4/6). Thus, the least common multiple of the denominators 5, 20, and 6 is 60. Thus, the given fractions can be written as 36/60, 27/60, 40/60. Therefore, we can conclude that 27/60 < 36/60 < 40/60.

Important Notes

• A denominator can never be zero.
• The concept of the least common denominator for fractions is used to evaluate the result as a part of the whole.

Topics Related to Least Common Denominator

• Common Denominator
• What is the lowest common denominator of 8 and 9?
• Numerator and Denominator Calculator
• Common Denominator Calculator
• Least Common Denominator Worksheets
• Rationalize the Denominator