Least Common Denominator

If the denominators are unlike, then we can find LCD (Least common Denominator) of the given denominators.

Least Common Denominator is the smallest positive(least) integer which is common in multiples of the denominators.

For example, given fractions are 1/3 and 1/6. Find LCD.

List the multiples of 3:   3, 6, 9, 12, 15, 18, 21,...

Multiples of 6:   6, 12, 18, 24,...

Here, 6 is the lowest common term for both the multiples of 3 and multiples of 6.

The answer is 6, and that is the Least Common Denominator.

There are five examples for least common denominator. From these examples for least common denominator, we can get clear view about least common denominator. Let us see the examples for least common denominator in the following section.

Examples on examples for least common denominator:

We are going to explain examples for least common denominator.

Example 1:

Find the least common denominator of the fractions; 1/5,1/3

Solution:

Here, the denominators are 5 and 3.

The common denominator of 5 and 3 is 15.

Multiples of 5: 5,10,15,20,…..

Multiples of 3: 3,6,9,12,15,18,….

Here, 15 is the lowest common term for both the multiples of 5 and multiples of 3.

The answer is 15, and that is the Least Common Denominator.

Example 2:

If the given fractions are 3/4,1/3, find the least common denominator.

Solution:

Here, the denominators are 4 and 3.

The common denominator of 4 and 3 is 12.

Multiples of 4: 4,8,12,16,20….

Multiples of 3: 3,6,9,12,15….

Here, 12 is the lowest common term for both the multiples of 4 and multiples of 3.

So, the Least Common Denominator is 12.

Example 3:

Find the least common denominator of ; 5/6, 2/15

Solution:

Here, the denominators are 6 and 15.

The common denominator of 6 and 15 is 30.

Multiples of 6:  6,12,18,24,30…

Multiples of 15: 15,30,45,60….

Here, 30 is the lowest common term for both the multiples of 6 and multiples of 15.

So, the Least common denominator is 30.

Example 4 on examples for least common denominator:

What is the least common denominator of the fractions;  5/12, 11/18

Solution:

Here, the denominators are 12 and 18.

The common denominator of 12 and 18 is 36.

Multiples of 12:  12,24,36,48,….

Multiples of 18: 18,36,54,….

Here, 36 is the lowest common term for both the multiples of 12 and multiples of 18.

So, the Least common denominator is 36.

Example 5:

1/5 + 1/6 + 1/15  What is the LCD?

Solution:

First we list the multiples of each denominator.

Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...

Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...

Multiples of 15 are 30, 45, 60, 75, 90,....

Here, 30 is the lowest common term for both the multiples of 5 and multiples of 6 and multiples of 15 .

So, the Least common denominator is 30.

Therefore, Examples for least common denominator are explained.