What is the Least Common Multiple of 21204 and 21208?

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 21208 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 21208, than apply into the LCM equation.

GCF(21204,21208) = 4
LCM(21204,21208) = ( 21204 × 21208) / 4
LCM(21204,21208) = 449694432 / 4
LCM(21204,21208) = 112423608

Least Common Multiple (LCM) of 21204 and 21208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21204 and 21208. First we will calculate the prime factors of 21204 and 21208.

Prime Factorization of 21204

Prime Factorization of 21208

Now multiplying the highest exponent prime factors to calculate the LCM of 21204 and 21208.

LCM(21204,21208) = 2³ × 3² × 19¹ × 31¹ × 11¹ × 241¹
LCM(21204,21208) = 112423608