What is the Least Common Multiple of 150 and 180?

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 150 and 180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 150 and 180, than apply into the LCM equation.

GCF(150,180) = 30
LCM(150,180) = ( 150 × 180) / 30
LCM(150,180) = 27000 / 30
LCM(150,180) = 900

Least Common Multiple (LCM) of 150 and 180 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 150 and 180. First we will calculate the prime factors of 150 and 180.

Prime Factorization of 150

Prime Factorization of 180

Now multiplying the highest exponent prime factors to calculate the LCM of 150 and 180.

LCM(150,180) = 2² × 3² × 5²
LCM(150,180) = 900