What is the Least Common Multiple of 72120 and 72138?

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 72120 and 72138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72120 and 72138, than apply into the LCM equation.

GCF(72120,72138) = 6
LCM(72120,72138) = ( 72120 × 72138) / 6
LCM(72120,72138) = 5202592560 / 6
LCM(72120,72138) = 867098760

Least Common Multiple (LCM) of 72120 and 72138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72120 and 72138. First we will calculate the prime factors of 72120 and 72138.

Prime Factorization of 72120

Prime Factorization of 72138

Now multiplying the highest exponent prime factors to calculate the LCM of 72120 and 72138.

LCM(72120,72138) = 2³ × 3¹ × 5¹ × 601¹ × 11¹ × 1093¹
LCM(72120,72138) = 867098760