What is the Least Common Multiple of 21204 and 21224?

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 21224 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 21224, than apply into the LCM equation.

GCF(21204,21224) = 4
LCM(21204,21224) = ( 21204 × 21224) / 4
LCM(21204,21224) = 450033696 / 4
LCM(21204,21224) = 112508424

Least Common Multiple (LCM) of 21204 and 21224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21204 and 21224. First we will calculate the prime factors of 21204 and 21224.

Prime Factorization of 21204

Prime Factorization of 21224

Now multiplying the highest exponent prime factors to calculate the LCM of 21204 and 21224.

LCM(21204,21224) = 2³ × 3² × 19¹ × 31¹ × 7¹ × 379¹
LCM(21204,21224) = 112508424