What is the Least Common Multiple of 8625 and 8640?

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 8625 and 8640 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8625 and 8640, than apply into the LCM equation.

GCF(8625,8640) = 15
LCM(8625,8640) = ( 8625 × 8640) / 15
LCM(8625,8640) = 74520000 / 15
LCM(8625,8640) = 4968000

Least Common Multiple (LCM) of 8625 and 8640 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8625 and 8640. First we will calculate the prime factors of 8625 and 8640.

Prime Factorization of 8625

Prime Factorization of 8640

Now multiplying the highest exponent prime factors to calculate the LCM of 8625 and 8640.

LCM(8625,8640) = 3³ × 5³ × 23¹ × 2⁶
LCM(8625,8640) = 4968000