What is the Least Common Multiple of 39660 and 39675?

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 39660 and 39675 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39660 and 39675, than apply into the LCM equation.

GCF(39660,39675) = 15
LCM(39660,39675) = ( 39660 × 39675) / 15
LCM(39660,39675) = 1573510500 / 15
LCM(39660,39675) = 104900700

Least Common Multiple (LCM) of 39660 and 39675 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39660 and 39675. First we will calculate the prime factors of 39660 and 39675.

Prime Factorization of 39660

Prime Factorization of 39675

Now multiplying the highest exponent prime factors to calculate the LCM of 39660 and 39675.

LCM(39660,39675) = 2² × 3¹ × 5² × 661¹ × 23²
LCM(39660,39675) = 104900700