What is the Least Common Multiple of 180 and 225?

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 of 180 and 225 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 180 and 225, than apply into the LCM equation.

GCF(180,225) = 45
LCM(180,225) = ( 180 × 225) / 45
LCM(180,225) = 40500 / 45
LCM(180,225) = 900

Least Common Multiple (LCM) of 180 and 225 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 180 and 225. First we will calculate the prime factors of 180 and 225.

Prime Factorization of 180

Prime Factorization of 225

Now multiplying the highest exponent prime factors to calculate the LCM of 180 and 225.

LCM(180,225) = 2² × 3² × 5²
LCM(180,225) = 900