# What is the Least Common Multiple of 21 and 36?

*Least common multiple* or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 21 and 36 is **252**.

LCM(21,36) = 252

## Least Common Multiple of 21 and 36 with GCF Formula

The formula of **LCM** is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 21 and 36, than apply into the LCM equation.

GCF(21,36) = 3

LCM(21,36) = ( 21 × 36) / 3

LCM(21,36) = 756 / 3

LCM(21,36) = 252

## Least Common Multiple (LCM) of 21 and 36 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 36. First we will calculate the **prime factors of 21 and 36**.

### Prime Factorization of 21

Prime factors of 21 are 3, 7. Prime factorization of **21** in exponential form is:

21 = 3^{1} × 7^{1}

### Prime Factorization of 36

Prime factors of 36 are 2, 3. Prime factorization of **36** in exponential form is:

36 = 2^{2} × 3^{2}

Now multiplying the highest exponent prime factors to calculate the **LCM of 21 and 36**.

LCM(21,36) = 3^{2} × 7^{1} × 2^{2}

LCM(21,36) = 252