What is the Least Common Multiple of 21375 and 21384?

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 21375 and 21384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21375 and 21384, than apply into the LCM equation.

GCF(21375,21384) = 9
LCM(21375,21384) = ( 21375 × 21384) / 9
LCM(21375,21384) = 457083000 / 9
LCM(21375,21384) = 50787000

Least Common Multiple (LCM) of 21375 and 21384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21375 and 21384. First we will calculate the prime factors of 21375 and 21384.

Prime Factorization of 21375

Prime Factorization of 21384

Now multiplying the highest exponent prime factors to calculate the LCM of 21375 and 21384.

LCM(21375,21384) = 3⁵ × 5³ × 19¹ × 2³ × 11¹
LCM(21375,21384) = 50787000