What is the Least Common Multiple of 75165 and 75180?

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 75165 and 75180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75165 and 75180, than apply into the LCM equation.

GCF(75165,75180) = 15
LCM(75165,75180) = ( 75165 × 75180) / 15
LCM(75165,75180) = 5650904700 / 15
LCM(75165,75180) = 376726980

Least Common Multiple (LCM) of 75165 and 75180 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75165 and 75180. First we will calculate the prime factors of 75165 and 75180.

Prime Factorization of 75165

Prime Factorization of 75180

Now multiplying the highest exponent prime factors to calculate the LCM of 75165 and 75180.

LCM(75165,75180) = 3¹ × 5¹ × 5011¹ × 2² × 7¹ × 179¹
LCM(75165,75180) = 376726980