Least Common Multiple  of 21 and 30 is 210

How to find the Least Common Multiple of 21 and 30?

On this page below, we'll use the Prime Factorisation, and the List of Multiples method to find out the LCM of 21 and 30.

Follow the steps below, and let's calculate the LCM of 21 and 30.


Method 1 - Prime factorization

Step 1: Create a list of all the prime factors of the numbers 21 and 30:

Prime factors of 21

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

21 = 31x71

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:

31, 71, 21, 51


Step 3: Multiply these values together:

31x71x21x51=210


Step 4: The result:

As seen on the calculation above, we have now obtained the LCM of 21 and 30.

The Least Common Multiple of 21 and 30 is 210.


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 21:

21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273

Multiples of 30:

30, 60, 90, 120, 150, 180, 210, 240, 270, 300


Therefore,

LCM(21, 30) = 210