# What is the Least Common Multiple of 5 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 5 and 21 is **105**.

LCM(5,21) = 105

## Least Common Multiple of 5 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 5 and 21, than apply into the LCM equation.

GCF(5,21) = 1

LCM(5,21) = ( 5 × 21) / 1

LCM(5,21) = 105 / 1

LCM(5,21) = 105

## Least Common Multiple (LCM) of 5 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 21. First we will calculate the **prime factors of 5 and 21**.

### Prime Factorization of 5

Prime factors of 5 are 5. Prime factorization of **5** in exponential form is:

5 = 5^{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 5 and 21**.

LCM(5,21) = 5^{1} × 3^{1} × 7^{1}

LCM(5,21) = 105