What is the Least Common Multiple of 75108 and 75117?

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 75117 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 75117, than apply into the LCM equation.

GCF(75108,75117) = 3
LCM(75108,75117) = ( 75108 × 75117) / 3
LCM(75108,75117) = 5641887636 / 3
LCM(75108,75117) = 1880629212

Least Common Multiple (LCM) of 75108 and 75117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75108 and 75117. First we will calculate the prime factors of 75108 and 75117.

Prime Factorization of 75108

Prime Factorization of 75117

Now multiplying the highest exponent prime factors to calculate the LCM of 75108 and 75117.

LCM(75108,75117) = 2² × 3¹ × 11¹ × 569¹ × 7³ × 73¹
LCM(75108,75117) = 1880629212