Least Common Multiple  of 9 and 12 is 36

How to find the Least Common Multiple of 9 and 12?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 9 and 12.

Follow the steps below, and let's calculate the LCM of 9 and 12.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 9 and 12:

Prime factors of 9

The prime factors of 9 are 3 and 3. Prime factorization of 9 in exponential form is:

9 = 32

Prime factors of 12

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

12 = 22x31


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

32, 22


Step 3: Multiply these values together:

32x22=36


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 9 and 12.

The Least Common Multiple of 9 and 12 is 36.


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 9:

9, 18, 27, 36, 45, 54, 63

Multiples of 12:

12, 24, 36, 48, 60, 72


Therefore,

LCM(9, 12) = 36