Least Common Multiple  of 30 and 36 is 180

How to find the Least Common Multiple of 30 and 36?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 30 and 36.

Follow the steps below, and let's calculate the LCM of 30 and 36.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 30 and 36:

Prime factors of 30

The prime factors of 30 are 2, 3 and 5. Prime factorization of 30 in exponential form is:

30 = 21x31x51

Prime factors of 36

The prime factors of 36 are 2, 2, 3 and 3. Prime factorization of 36 in exponential form is:

36 = 22x32


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

22, 32, 51


Step 3: Multiply these values together:

22x32x51=180


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 30 and 36.

The Least Common Multiple of 30 and 36 is 180.


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 30:

30, 60, 90, 120, 150, 180, 210, 240, 270

Multiples of 36:

36, 72, 108, 144, 180, 216, 252, 288


Therefore,

LCM(30, 36) = 180