What is the Least Common Multiple of 39108 and 39123?

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 39108 and 39123 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39108 and 39123, than apply into the LCM equation.

GCF(39108,39123) = 3
LCM(39108,39123) = ( 39108 × 39123) / 3
LCM(39108,39123) = 1530022284 / 3
LCM(39108,39123) = 510007428

Least Common Multiple (LCM) of 39108 and 39123 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39108 and 39123. First we will calculate the prime factors of 39108 and 39123.

Prime Factorization of 39108

Prime Factorization of 39123

Now multiplying the highest exponent prime factors to calculate the LCM of 39108 and 39123.

LCM(39108,39123) = 2² × 3⁵ × 3259¹ × 7¹ × 23¹
LCM(39108,39123) = 510007428