# What is the Least Common Multiple of 5 and 9?

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 5 and 9 is 45.

LCM(5,9) = 45

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## Least Common Multiple of 5 and 9 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 9, than apply into the LCM equation.

GCF(5,9) = 1
LCM(5,9) = ( 5 × 9) / 1
LCM(5,9) = 45 / 1
LCM(5,9) = 45

## Least Common Multiple (LCM) of 5 and 9 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 9. First we will calculate the prime factors of 5 and 9.

### Prime Factorization of 5

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

5 = 51

### Prime Factorization of 9

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

9 = 32

Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 9.

LCM(5,9) = 51 × 32
LCM(5,9) = 45