# What is the LCM of 12, 15 and 45?

LCM of 12, 15 and 45 is the smallest number that is exactly divisible by three of them.

## Answer: LCM of 12, 15 and 45 is 180.

Let us see how to find the LCM of 12, 15 and 45

## Explanation:

Least Common Multiple is the smallest number that will divide 12, 15 and 45 exactly without a remainder.

Let us see how to calculate it below:

### LCM of 12, 15, and 45 by Division Method:

In this division method, we divide 12, 15 and 45 simultaneously with prime numbers and stop it when we don't have a prime number to divide them further.THe product of these prime numbers is the LCM of 12 ,15 and 45.

### LCM of 12, 15, and 45 using Prime Factorization:

Write all the given numbers as the product of its prime factors

Prime factorization of 12 = 2 x 2 x 3 = 2^{2} x 3,

**15** = 5 x 3 , and

**45** = 3 x 3 x 5 = 3^{2} x 5

The prime factors 2 and 3 occur twice and the prime factor 5 occurs one time in the prime factorization.

So, the product of all these prime factors is 2^{2} x 3^{2} x 5= 180