What is the Least Common Multiple of 17625 and 17640?

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 17625 and 17640 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17625 and 17640, than apply into the LCM equation.

GCF(17625,17640) = 15
LCM(17625,17640) = ( 17625 × 17640) / 15
LCM(17625,17640) = 310905000 / 15
LCM(17625,17640) = 20727000

Least Common Multiple (LCM) of 17625 and 17640 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17625 and 17640. First we will calculate the prime factors of 17625 and 17640.

Prime Factorization of 17625

Prime Factorization of 17640

Now multiplying the highest exponent prime factors to calculate the LCM of 17625 and 17640.

LCM(17625,17640) = 3² × 5³ × 47¹ × 2³ × 7²
LCM(17625,17640) = 20727000