What is the Least Common Multiple of 21204 and 21219?

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 21204 and 21219 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21204 and 21219, than apply into the LCM equation.

GCF(21204,21219) = 3
LCM(21204,21219) = ( 21204 × 21219) / 3
LCM(21204,21219) = 449927676 / 3
LCM(21204,21219) = 149975892

Least Common Multiple (LCM) of 21204 and 21219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21204 and 21219. First we will calculate the prime factors of 21204 and 21219.

Prime Factorization of 21204

Prime Factorization of 21219

Now multiplying the highest exponent prime factors to calculate the LCM of 21204 and 21219.

LCM(21204,21219) = 2² × 3² × 19¹ × 31¹ × 11¹ × 643¹
LCM(21204,21219) = 149975892