What is the Least Common Multiple of 75585 and 75600?

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 75585 and 75600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75585 and 75600, than apply into the LCM equation.

GCF(75585,75600) = 15
LCM(75585,75600) = ( 75585 × 75600) / 15
LCM(75585,75600) = 5714226000 / 15
LCM(75585,75600) = 380948400

Least Common Multiple (LCM) of 75585 and 75600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75585 and 75600. First we will calculate the prime factors of 75585 and 75600.

Prime Factorization of 75585

Prime Factorization of 75600

Now multiplying the highest exponent prime factors to calculate the LCM of 75585 and 75600.

LCM(75585,75600) = 3³ × 5² × 5039¹ × 2⁴ × 7¹
LCM(75585,75600) = 380948400