What is the Least Common Multiple of 72096 and 72114?

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 72096 and 72114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72096 and 72114, than apply into the LCM equation.

GCF(72096,72114) = 6
LCM(72096,72114) = ( 72096 × 72114) / 6
LCM(72096,72114) = 5199130944 / 6
LCM(72096,72114) = 866521824

Least Common Multiple (LCM) of 72096 and 72114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72096 and 72114. First we will calculate the prime factors of 72096 and 72114.

Prime Factorization of 72096

Prime Factorization of 72114

Now multiplying the highest exponent prime factors to calculate the LCM of 72096 and 72114.

LCM(72096,72114) = 2⁵ × 3¹ × 751¹ × 7¹ × 17¹ × 101¹
LCM(72096,72114) = 866521824