# What is the LCM of 8, 12 and 15?

LCM of 8, 12 and 15 is the smallest number which is exactly divisible by all of them.

## Answer: LCM of 8, 12 and 15 is 30

Let us see how to find the LCM of 8, 12 and 15

## Explanation:

We can find the LCM by the following two methods:

- by Division Method
- using Common Multiples

Least Common Multiple of 8, 12 and 15 will be the smallest number that exactly divides all of them without leaving a remainder.

We will explain two methods to find the LCM of 8, 12 and 15

## Methods to Find LCM of 8, 12 and 15

### Method 1: LCM of 8, 12 and 15 by Division Method:

In this division method, we divide 8, 12 and 15 simultaneously with prime numbers and stop it when we don't have a prime number to divide 8,12 and 15 any further.

So, the least common multiple of 8, 12 and 15 is given by 2 × 2 × 2 × 3 × 5 = 120. This means LCM(8, 12, 15) = 120

### Method 2: LCM of 8, 12 and 15 using Common Multiples:

Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135

Clearly, 120 is the least common factor of 8, 12 and 15

Hence, LCM of 8, 12 and 15 = 70