What is the Least Common Multiple of 21312 and 21328?

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 21312 and 21328 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21312 and 21328, than apply into the LCM equation.

GCF(21312,21328) = 16
LCM(21312,21328) = ( 21312 × 21328) / 16
LCM(21312,21328) = 454542336 / 16
LCM(21312,21328) = 28408896

Least Common Multiple (LCM) of 21312 and 21328 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21312 and 21328. First we will calculate the prime factors of 21312 and 21328.

Prime Factorization of 21312

Prime Factorization of 21328

Now multiplying the highest exponent prime factors to calculate the LCM of 21312 and 21328.

LCM(21312,21328) = 2⁶ × 3² × 37¹ × 31¹ × 43¹
LCM(21312,21328) = 28408896