What is the Least Common Multiple of 75096 and 75114?

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 75096 and 75114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75096 and 75114, than apply into the LCM equation.

GCF(75096,75114) = 18
LCM(75096,75114) = ( 75096 × 75114) / 18
LCM(75096,75114) = 5640760944 / 18
LCM(75096,75114) = 313375608

Least Common Multiple (LCM) of 75096 and 75114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75096 and 75114. First we will calculate the prime factors of 75096 and 75114.

Prime Factorization of 75096

Prime Factorization of 75114

Now multiplying the highest exponent prime factors to calculate the LCM of 75096 and 75114.

LCM(75096,75114) = 2³ × 3³ × 7¹ × 149¹ × 13¹ × 107¹
LCM(75096,75114) = 313375608