What is the Least Common Multiple of 21360 and 21375?

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 21360 and 21375 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21360 and 21375, than apply into the LCM equation.

GCF(21360,21375) = 15
LCM(21360,21375) = ( 21360 × 21375) / 15
LCM(21360,21375) = 456570000 / 15
LCM(21360,21375) = 30438000

Least Common Multiple (LCM) of 21360 and 21375 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21360 and 21375. First we will calculate the prime factors of 21360 and 21375.

Prime Factorization of 21360

Prime Factorization of 21375

Now multiplying the highest exponent prime factors to calculate the LCM of 21360 and 21375.

LCM(21360,21375) = 2⁴ × 3² × 5³ × 89¹ × 19¹
LCM(21360,21375) = 30438000