# What is the Least Common Multiple of 8 and 15?

*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 8 and 15 is **120**.

LCM(8,15) = 120

## Least Common Multiple of 8 and 15 with GCF Formula

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

We need to calculate greatest common factor 8 and 15, than apply into the LCM equation.

GCF(8,15) = 1

LCM(8,15) = ( 8 × 15) / 1

LCM(8,15) = 120 / 1

LCM(8,15) = 120

## Least Common Multiple (LCM) of 8 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 15. First we will calculate the **prime factors of 8 and 15**.

### Prime Factorization of 8

Prime factors of 8 are 2. Prime factorization of **8** in exponential form is:

8 = 2^{3}

### Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of **15** in exponential form is:

15 = 3^{1} × 5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 8 and 15**.

LCM(8,15) = 2^{3} × 3^{1} × 5^{1}

LCM(8,15) = 120