# What is the Least Common Multiple of 10 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 10 and 15 is 30.

LCM(10,15) = 30

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## Least Common Multiple of 10 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 10 and 15, than apply into the LCM equation.

GCF(10,15) = 5
LCM(10,15) = ( 10 × 15) / 5
LCM(10,15) = 150 / 5
LCM(10,15) = 30

## Least Common Multiple (LCM) of 10 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 15. First we will calculate the prime factors of 10 and 15.

### Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:

10 = 21 × 51

### 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 10 and 15.

LCM(10,15) = 21 × 51 × 31
LCM(10,15) = 30