# What is the Least Common Multiple of 3 and 10?

*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 3 and 10 is **30**.

LCM(3,10) = 30

## Least Common Multiple of 3 and 10 with GCF Formula

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

We need to calculate greatest common factor 3 and 10, than apply into the LCM equation.

GCF(3,10) = 1

LCM(3,10) = ( 3 × 10) / 1

LCM(3,10) = 30 / 1

LCM(3,10) = 30

## Least Common Multiple (LCM) of 3 and 10 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 10. First we will calculate the **prime factors of 3 and 10**.

### Prime Factorization of 3

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

3 = 3^{1}

### Prime Factorization of 10

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

10 = 2^{1} × 5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 3 and 10**.

LCM(3,10) = 3^{1} × 2^{1} × 5^{1}

LCM(3,10) = 30