What is the Least Common Multiple of 48120 and 48138?

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 48120 and 48138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48120 and 48138, than apply into the LCM equation.

GCF(48120,48138) = 6
LCM(48120,48138) = ( 48120 × 48138) / 6
LCM(48120,48138) = 2316400560 / 6
LCM(48120,48138) = 386066760

Least Common Multiple (LCM) of 48120 and 48138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 48120 and 48138. First we will calculate the prime factors of 48120 and 48138.

Prime Factorization of 48120

Prime Factorization of 48138

Now multiplying the highest exponent prime factors to calculate the LCM of 48120 and 48138.

LCM(48120,48138) = 2³ × 3¹ × 5¹ × 401¹ × 71¹ × 113¹
LCM(48120,48138) = 386066760