Find the LCM Using Prime Factors

In this activity, we will be finding the Lowest Common Multiple or the LCM for given values. 

For smaller values we can do this by listing all of the factors for given numbers. However, this becomes an arduous task when we have larger values. 

Instead, we can do this by comparing the product of prime factors of the values given.

Example

Find the LCM of 36 and 198.

First, we start by writing 36 and 198 as products of their prime factors.

36 = 2 x 2 x 3 x 3

198 = 2 x 3 x 3 x 11

To find the LCM we multiply together the prime factors that appear in either list.

Start by listing the prime factors for 36: 2 x 2 x 3 x 3

Now add any prime factors for 198 that haven't already been included - we've already used 2 x 3 x 3, so we only have 11 to add.

This gives us 2 x 2 x 3 x 3 x 11 as the prime factors that appear in either list.

Finally, multiply all those together: 2 x 2 x 3 x 3 x 11 = 396

The LCM of 36 and 198 = 396

Example 2

Find the LCM of 120 and 155.

First, we start by writing 120 and 155 as products of their prime factors.

120 = 2 x 2 x 2 x 3 x 5

155 = 5 x 31

The prime factors that appear in either list are: 2 x 2 x 2 x 3 x 5 (from 120) and 31 (from 155)

2 x 2 x 2 x 3 x 5 x 31 = 3,720

Remember that you can check back to these instructions at any point by clicking on the red button at the side of the screen.