 ## How to find the Least Common Multiple of 12 and 21?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 12 and 21.

Follow the steps below, and let's calculate the LCM of 12 and 21.

### Method 1 - Prime factorization

#### Step 1: Create a list of all the prime factors of the numbers 12 and 21:

##### Prime factors of 12

The prime factors of 12 are 2, 2 and 3. Prime factorization of 12 in exponential form is:

12 = 22x31

##### Prime factors of 21

The prime factors of 21 are 3 and 7. Prime factorization of 21 in exponential form is:

21 = 31x71

22, 31, 71

22x31x71=84

#### Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 12 and 21.

The Least Common Multiple of 12 and 21 is 84.

### Method 2 - List of Multiples

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

#### Multiples of 12:

12, 24, 36, 48, 60, 72, 84, 96, 108, 120

#### Multiples of 21:

21, 42, 63, 84, 105, 126, 147

LCM(12, 21) = 84