Least Common Multiple  of 12 and 21 is 84

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


Step 2: Identify the highest power of each prime number from the above boxes:

22, 31, 71


Step 3: Multiply these values together:

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


Therefore,

LCM(12, 21) = 84