What is the Least Common Multiple of 21312 and 21330?

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 21330 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 21330, than apply into the LCM equation.

GCF(21312,21330) = 18
LCM(21312,21330) = ( 21312 × 21330) / 18
LCM(21312,21330) = 454584960 / 18
LCM(21312,21330) = 25254720

Least Common Multiple (LCM) of 21312 and 21330 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21312 and 21330. First we will calculate the prime factors of 21312 and 21330.

Prime Factorization of 21312

Prime Factorization of 21330

Now multiplying the highest exponent prime factors to calculate the LCM of 21312 and 21330.

LCM(21312,21330) = 2⁶ × 3³ × 37¹ × 5¹ × 79¹
LCM(21312,21330) = 25254720