What is the Least Common Multiple of 6123 and 6132?

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 6123 and 6132 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6123 and 6132, than apply into the LCM equation.

GCF(6123,6132) = 3
LCM(6123,6132) = ( 6123 × 6132) / 3
LCM(6123,6132) = 37546236 / 3
LCM(6123,6132) = 12515412

Least Common Multiple (LCM) of 6123 and 6132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6123 and 6132. First we will calculate the prime factors of 6123 and 6132.

Prime Factorization of 6123

Prime Factorization of 6132

Now multiplying the highest exponent prime factors to calculate the LCM of 6123 and 6132.

LCM(6123,6132) = 3¹ × 13¹ × 157¹ × 2² × 7¹ × 73¹
LCM(6123,6132) = 12515412