# Least Common Multiple of 7 and 12

Least common multiple (LCM) of 7 and 12 is 84.

LCM(7,12) = 84

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.

LCM Calculator and

## Least Common Multiple of 7 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 7 and 12, than apply into the LCM equation.

GCF(7,12) = 1
LCM(7,12) = ( 7 × 12) / 1
LCM(7,12) = 84 / 1
LCM(7,12) = 84

## Least Common Multiple (LCM) of 7 and 12 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 12. First we will calculate the prime factors of 7 and 12.

### Prime Factorization of 7

Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:

7 = 71

### 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 7 and 12.

LCM(7,12) = 71 × 22 × 31
LCM(7,12) = 84