# What is the LCM of 12, 16, and 18?

LCM of 12, 16, and 18 is the least number which is exactly divisible by 12, 16, and 18.

## Answer: LCM of 12, 16, and 18 is 144

Let us see the explanation of why LCM(12,16,18) is 144.

## Explanation:

We will use the following 2 methods to find LCM of 12, 16 and 18

- Common Division
- Listing the common multiples

### Method 1: LCM of 12, 16 and 18 by Common Division Method

In this division method, we divide the 12, 16 and 18 simultaneously with prime numbers and stop it when we don't have a prime number to divide both 12, 16 and 18.

LCM(12, 16, 18) = 2 × 2 × 2 × 2 × 3 × 3 = 144

### Method 2: LCM of 12, 16 and 18 by Listing Common Multiples

Let us list the first few multiples of 12,16 and 18 and identify the first number which is a multiple of all 3.

Multiples of 12 = 12, 24, 36, 48, 60, 72, 78, 84, 96, 108, 120, 132, **144**, 156, 168,...

Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, , 160, 176**144**,...

Mutiples of 18 = 18, 36, 54, 72, 90, 108, 126, **144**, 162, 180,...

We see that 144 is the first number which is a multiple of 12,16 and 18.