# What is the Least Common Multiple of 9 and 20?

*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 9 and 20 is **180**.

LCM(9,20) = 180

## Least Common Multiple of 9 and 20 with GCF Formula

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

We need to calculate greatest common factor 9 and 20, than apply into the LCM equation.

GCF(9,20) = 1

LCM(9,20) = ( 9 × 20) / 1

LCM(9,20) = 180 / 1

LCM(9,20) = 180

## Least Common Multiple (LCM) of 9 and 20 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 20. First we will calculate the **prime factors of 9 and 20**.

### Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of **9** in exponential form is:

9 = 3^{2}

### Prime Factorization of 20

Prime factors of 20 are 2, 5. Prime factorization of **20** in exponential form is:

20 = 2^{2} × 5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 9 and 20**.

LCM(9,20) = 3^{2} × 2^{2} × 5^{1}

LCM(9,20) = 180