What is the Least Common Multiple of 21198 and 21216?

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 21198 and 21216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21198 and 21216, than apply into the LCM equation.

GCF(21198,21216) = 6
LCM(21198,21216) = ( 21198 × 21216) / 6
LCM(21198,21216) = 449736768 / 6
LCM(21198,21216) = 74956128

Least Common Multiple (LCM) of 21198 and 21216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21198 and 21216. First we will calculate the prime factors of 21198 and 21216.

Prime Factorization of 21198

Prime Factorization of 21216

Now multiplying the highest exponent prime factors to calculate the LCM of 21198 and 21216.

LCM(21198,21216) = 2⁵ × 3¹ × 3533¹ × 13¹ × 17¹
LCM(21198,21216) = 74956128