# What is the LCM of 60, 84 and 108?

LCM of 60,84 and 108 is the least (smallest) number which is exactly divisible by the given set of numbers.

## Answer: LCM of 60, 84 and 108 is 3780

Let us see how to find the LCM 60, 84 and 108

## Explanation:

We will use the following two methods to Find the LCM of 60,84 and 108

- LCM of 60, 84 and 108 by Prime Factorization
- LCM of 60, 84 and 108 by Long Division

### Method 1: LCM of 60, 84 and 108 by Prime Factorization

Steps to find LCM by using prime factorization are given below.

**Step 1: **Write the prime factorized form which must be in exponential notation.

**Step 2:** Take the product of factors with their highest power.

Prime Factorised form of 60: 2^{2 }× 3 × 5

Prime Factorised form of 84: 2^{2 }× 3 × 7

Prime Factorised form of 108: 2^{2 }× 3^{3}

Therefore LCM of 60, 84 and 108 would be 2^{2 }× 3^{3 }× 5 × 7 = 3780

### Method 2: LCM of 60, 84 and 108 by Long Division

In this division method, we divide the numbers parallelly with prime numbers and stop until we don't have a prime number to divide the given numbers.The product of all the prime numbers used for division is the LCM of given set of numbers.

Irrespective of the method, the solution to our question is the same.