What is the Least Common Multiple of 75180 and 75189?

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 75180 and 75189 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75180 and 75189, than apply into the LCM equation.

GCF(75180,75189) = 3
LCM(75180,75189) = ( 75180 × 75189) / 3
LCM(75180,75189) = 5652709020 / 3
LCM(75180,75189) = 1884236340

Least Common Multiple (LCM) of 75180 and 75189 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75180 and 75189. First we will calculate the prime factors of 75180 and 75189.

Prime Factorization of 75180

Prime Factorization of 75189

Now multiplying the highest exponent prime factors to calculate the LCM of 75180 and 75189.

LCM(75180,75189) = 2² × 3¹ × 5¹ × 7¹ × 179¹ × 71¹ × 353¹
LCM(75180,75189) = 1884236340