What is the Least Common Multiple of 54105 and 54123?

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 54105 and 54123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54105 and 54123, than apply into the LCM equation.

GCF(54105,54123) = 3
LCM(54105,54123) = ( 54105 × 54123) / 3
LCM(54105,54123) = 2928324915 / 3
LCM(54105,54123) = 976108305

Least Common Multiple (LCM) of 54105 and 54123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54105 and 54123. First we will calculate the prime factors of 54105 and 54123.

Prime Factorization of 54105

Prime Factorization of 54123

Now multiplying the highest exponent prime factors to calculate the LCM of 54105 and 54123.

LCM(54105,54123) = 3¹ × 5¹ × 3607¹ × 18041¹
LCM(54105,54123) = 976108305