What is the Least Common Multiple of 51096 and 51114?

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 51096 and 51114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51096 and 51114, than apply into the LCM equation.

GCF(51096,51114) = 6
LCM(51096,51114) = ( 51096 × 51114) / 6
LCM(51096,51114) = 2611720944 / 6
LCM(51096,51114) = 435286824

Least Common Multiple (LCM) of 51096 and 51114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51096 and 51114. First we will calculate the prime factors of 51096 and 51114.

Prime Factorization of 51096

Prime Factorization of 51114

Now multiplying the highest exponent prime factors to calculate the LCM of 51096 and 51114.

LCM(51096,51114) = 2³ × 3¹ × 2129¹ × 7¹ × 1217¹
LCM(51096,51114) = 435286824