What is the Least Common Multiple of 21660 and 21675?

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 21660 and 21675 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21660 and 21675, than apply into the LCM equation.

GCF(21660,21675) = 15
LCM(21660,21675) = ( 21660 × 21675) / 15
LCM(21660,21675) = 469480500 / 15
LCM(21660,21675) = 31298700

Least Common Multiple (LCM) of 21660 and 21675 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21660 and 21675. First we will calculate the prime factors of 21660 and 21675.

Prime Factorization of 21660

Prime Factorization of 21675

Now multiplying the highest exponent prime factors to calculate the LCM of 21660 and 21675.

LCM(21660,21675) = 2² × 3¹ × 5² × 19² × 17²
LCM(21660,21675) = 31298700