# What is the Least Common Multiple of 6 and 21?

*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 6 and 21 is **42**.

LCM(6,21) = 42

## Least Common Multiple of 6 and 21 with GCF Formula

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

We need to calculate greatest common factor 6 and 21, than apply into the LCM equation.

GCF(6,21) = 3

LCM(6,21) = ( 6 × 21) / 3

LCM(6,21) = 126 / 3

LCM(6,21) = 42

## Least Common Multiple (LCM) of 6 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 21. First we will calculate the **prime factors of 6 and 21**.

### Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of **6** in exponential form is:

6 = 2^{1} × 3^{1}

### Prime Factorization of 21

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

21 = 3^{1} × 7^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 6 and 21**.

LCM(6,21) = 2^{1} × 3^{1} × 7^{1}

LCM(6,21) = 42