# What is the Least Common Multiple of 3 and 18?

*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 18 is **18**.

LCM(3,18) = 18

## Least Common Multiple of 3 and 18 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 18, than apply into the LCM equation.

GCF(3,18) = 3

LCM(3,18) = ( 3 × 18) / 3

LCM(3,18) = 54 / 3

LCM(3,18) = 18

## Least Common Multiple (LCM) of 3 and 18 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 18. First we will calculate the **prime factors of 3 and 18**.

### Prime Factorization of 3

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

3 = 3^{1}

### Prime Factorization of 18

Prime factors of 18 are 2, 3. Prime factorization of **18** in exponential form is:

18 = 2^{1} × 3^{2}

Now multiplying the highest exponent prime factors to calculate the **LCM of 3 and 18**.

LCM(3,18) = 3^{2} × 2^{1}

LCM(3,18) = 18