Least Common Multiple  of 18 and 30 is 90

How to find the Least Common Multiple of 18 and 30?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 18 and 30.

Follow the steps below, and let's calculate the LCM of 18 and 30.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 18 and 30:

Prime factors of 18

The prime factors of 18 are 2, 3 and 3. Prime factorization of 18 in exponential form is:

18 = 21x32

Prime factors of 30

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

30 = 21x31x51


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

21, 32, 51


Step 3: Multiply these values together:

21x32x51=90


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 18 and 30.

The Least Common Multiple of 18 and 30 is 90.


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 18:

18, 36, 54, 72, 90, 108, 126, 144

Multiples of 30:

30, 60, 90, 120, 150, 180


Therefore,

LCM(18, 30) = 90