# What is the Least Common Multiple of 21 and 31?

*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 31 is **651**.

LCM(21,31) = 651

## Least Common Multiple of 21 and 31 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 31, than apply into the LCM equation.

GCF(21,31) = 1

LCM(21,31) = ( 21 × 31) / 1

LCM(21,31) = 651 / 1

LCM(21,31) = 651

## Least Common Multiple (LCM) of 21 and 31 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21 and 31. First we will calculate the **prime factors of 21 and 31**.

### 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 31

Prime factors of 31 are 31. Prime factorization of **31** in exponential form is:

31 = 31^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 21 and 31**.

LCM(21,31) = 3^{1} × 7^{1} × 31^{1}

LCM(21,31) = 651