What is the Least Common Multiple of 6105 and 6123?

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 6105 and 6123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6105 and 6123, than apply into the LCM equation.

GCF(6105,6123) = 3
LCM(6105,6123) = ( 6105 × 6123) / 3
LCM(6105,6123) = 37380915 / 3
LCM(6105,6123) = 12460305

Least Common Multiple (LCM) of 6105 and 6123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6105 and 6123. First we will calculate the prime factors of 6105 and 6123.

Prime Factorization of 6105

Prime Factorization of 6123

Now multiplying the highest exponent prime factors to calculate the LCM of 6105 and 6123.

LCM(6105,6123) = 3¹ × 5¹ × 11¹ × 37¹ × 13¹ × 157¹
LCM(6105,6123) = 12460305