What is the Least Common Multiple of 30123 and 30138?

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 30123 and 30138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30123 and 30138, than apply into the LCM equation.

GCF(30123,30138) = 3
LCM(30123,30138) = ( 30123 × 30138) / 3
LCM(30123,30138) = 907846974 / 3
LCM(30123,30138) = 302615658

Least Common Multiple (LCM) of 30123 and 30138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30123 and 30138. First we will calculate the prime factors of 30123 and 30138.

Prime Factorization of 30123

Prime Factorization of 30138

Now multiplying the highest exponent prime factors to calculate the LCM of 30123 and 30138.

LCM(30123,30138) = 3² × 3347¹ × 2¹ × 5023¹
LCM(30123,30138) = 302615658