What is the Least Common Multiple of 21216 and 21228?

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 21216 and 21228 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21216 and 21228, than apply into the LCM equation.

GCF(21216,21228) = 12
LCM(21216,21228) = ( 21216 × 21228) / 12
LCM(21216,21228) = 450373248 / 12
LCM(21216,21228) = 37531104

Least Common Multiple (LCM) of 21216 and 21228 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21216 and 21228. First we will calculate the prime factors of 21216 and 21228.

Prime Factorization of 21216

Prime Factorization of 21228

Now multiplying the highest exponent prime factors to calculate the LCM of 21216 and 21228.

LCM(21216,21228) = 2⁵ × 3¹ × 13¹ × 17¹ × 29¹ × 61¹
LCM(21216,21228) = 37531104