# What is the Least Common Multiple of 75 and 90?

*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 75 and 90 is **450**.

LCM(75,90) = 450

## Least Common Multiple of 75 and 90 with GCF Formula

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

We need to calculate greatest common factor 75 and 90, than apply into the LCM equation.

GCF(75,90) = 15

LCM(75,90) = ( 75 × 90) / 15

LCM(75,90) = 6750 / 15

LCM(75,90) = 450

## Least Common Multiple (LCM) of 75 and 90 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 90. First we will calculate the **prime factors of 75 and 90**.

### Prime Factorization of 75

Prime factors of 75 are 3, 5. Prime factorization of **75** in exponential form is:

75 = 3^{1} × 5^{2}

### Prime Factorization of 90

Prime factors of 90 are 2, 3, 5. Prime factorization of **90** in exponential form is:

90 = 2^{1} × 3^{2} × 5^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 75 and 90**.

LCM(75,90) = 3^{2} × 5^{2} × 2^{1}

LCM(75,90) = 450