# What is the Least Common Multiple of 30 and 39?

*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 30 and 39 is **390**.

LCM(30,39) = 390

## Least Common Multiple of 30 and 39 with GCF Formula

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

We need to calculate greatest common factor 30 and 39, than apply into the LCM equation.

GCF(30,39) = 3

LCM(30,39) = ( 30 × 39) / 3

LCM(30,39) = 1170 / 3

LCM(30,39) = 390

## Least Common Multiple (LCM) of 30 and 39 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 39. First we will calculate the **prime factors of 30 and 39**.

### Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of **30** in exponential form is:

30 = 2^{1} × 3^{1} × 5^{1}

### Prime Factorization of 39

Prime factors of 39 are 3, 13. Prime factorization of **39** in exponential form is:

39 = 3^{1} × 13^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 30 and 39**.

LCM(30,39) = 2^{1} × 3^{1} × 5^{1} × 13^{1}

LCM(30,39) = 390