What is the Least Common Multiple of 9120 and 9138?

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 9120 and 9138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9120 and 9138, than apply into the LCM equation.

GCF(9120,9138) = 6
LCM(9120,9138) = ( 9120 × 9138) / 6
LCM(9120,9138) = 83338560 / 6
LCM(9120,9138) = 13889760

Least Common Multiple (LCM) of 9120 and 9138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9120 and 9138. First we will calculate the prime factors of 9120 and 9138.

Prime Factorization of 9120

Prime Factorization of 9138

Now multiplying the highest exponent prime factors to calculate the LCM of 9120 and 9138.

LCM(9120,9138) = 2⁵ × 3¹ × 5¹ × 19¹ × 1523¹
LCM(9120,9138) = 13889760