# Least Common Multiple of 6 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 6 and 15 is 30.

LCM(6,15) = 30

LCM Calculator and

## Least Common Multiple of 6 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 6 and 15, than apply into the LCM equation.

GCF(6,15) = 3
LCM(6,15) = ( 6 × 15) / 3
LCM(6,15) = 90 / 3
LCM(6,15) = 30

## Least Common Multiple (LCM) of 6 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 15. First we will calculate the prime factors of 6 and 15.

### Prime Factorization of 6

Prime factors of 6 are 2, 3. Prime factorization of 6 in exponential form is:

6 = 21 × 31

### Prime Factorization of 15

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

15 = 31 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 15.

LCM(6,15) = 21 × 31 × 51
LCM(6,15) = 30