# What is the Least Common Multiple of 8 and 12?

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 12 is 24.

LCM(8,12) = 24

LCM Calculator and
and

## Least Common Multiple of 8 and 12 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 12, than apply into the LCM equation.

GCF(8,12) = 4
LCM(8,12) = ( 8 × 12) / 4
LCM(8,12) = 96 / 4
LCM(8,12) = 24

## Least Common Multiple (LCM) of 8 and 12 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 12. First we will calculate the prime factors of 8 and 12.

### Prime Factorization of 8

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

8 = 23

### Prime Factorization of 12

Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:

12 = 22 × 31

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 12.

LCM(8,12) = 23 × 31
LCM(8,12) = 24