What is the Least Common Multiple of 12204 and 12219?

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 12204 and 12219 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12204 and 12219, than apply into the LCM equation.

GCF(12204,12219) = 3
LCM(12204,12219) = ( 12204 × 12219) / 3
LCM(12204,12219) = 149120676 / 3
LCM(12204,12219) = 49706892

Least Common Multiple (LCM) of 12204 and 12219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12204 and 12219. First we will calculate the prime factors of 12204 and 12219.

Prime Factorization of 12204

Prime Factorization of 12219

Now multiplying the highest exponent prime factors to calculate the LCM of 12204 and 12219.

LCM(12204,12219) = 2² × 3³ × 113¹ × 4073¹
LCM(12204,12219) = 49706892