# 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

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## 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 = 32

### Prime Factorization of 20

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

20 = 22 × 51

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

LCM(9,20) = 32 × 22 × 51
LCM(9,20) = 180