What is the Least Common Multiple of 20625 and 20640?

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 20625 and 20640 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20625 and 20640, than apply into the LCM equation.

GCF(20625,20640) = 15
LCM(20625,20640) = ( 20625 × 20640) / 15
LCM(20625,20640) = 425700000 / 15
LCM(20625,20640) = 28380000

Least Common Multiple (LCM) of 20625 and 20640 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20625 and 20640. First we will calculate the prime factors of 20625 and 20640.

Prime Factorization of 20625

Prime Factorization of 20640

Now multiplying the highest exponent prime factors to calculate the LCM of 20625 and 20640.

LCM(20625,20640) = 3¹ × 5⁴ × 11¹ × 2⁵ × 43¹
LCM(20625,20640) = 28380000