# What is the LCM of 6, 9 and 15?

LCM of 6, 9 and 15 is the smallest number which exactly divides 6, 9 and 15 without leaving a remainder.

## Answer: LCM of 6, 9 and 15 is 90

The two methods that are used to find the LCM of 6, 9, and 15 are given below.

## Explanation:

For 6, 9 and 15 the smallest number which would be perfectly divisible by them is their LCM which is 90. We will use the following two methods to find the LCM of 6, 9 and 15:

- LCM of 6, 9 and 15 by Listing Method
- LCM of 6, 9 and 15 by Common Division Method

Least Common Multiple of 6, 9 and 15 is the smallest number that will divide 6, 9 and 15 exactly.

### Method1: LCM of 6, 9 and 15 by Listing Method

List the first few multiples of 6, 9 and 15 and find the common multiples.

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84,**90**,...,...

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, **90**, 99, 108,...

Multiples of 15: 15, 30, 45, 60, 75, **90**, 105 and 120,...

The smallest among the common multiples is the LCM of 6, 9 and 15, which in the above case we can see is 90. So, using the listing method, LCM of 6, 9 and 15 is 90

### Method2: LCM of 6, 9 and 15 by Common Division Method

Here we will divide the numbers 6, 9 and 15 simultaneously with prime numbers until we don't have a prime number to further divide both 6, 9 and 15

Observe that using any of the methods, we get the same answer to LCM (6, 9, 15)