What is the Least Common Multiple of 75108 and 75119?

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 75108 and 75119 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75108 and 75119, than apply into the LCM equation.

GCF(75108,75119) = 11
LCM(75108,75119) = ( 75108 × 75119) / 11
LCM(75108,75119) = 5642037852 / 11
LCM(75108,75119) = 512912532

Least Common Multiple (LCM) of 75108 and 75119 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75108 and 75119. First we will calculate the prime factors of 75108 and 75119.

Prime Factorization of 75108

Prime Factorization of 75119

Now multiplying the highest exponent prime factors to calculate the LCM of 75108 and 75119.

LCM(75108,75119) = 2² × 3¹ × 11¹ × 569¹ × 6829¹
LCM(75108,75119) = 512912532