What is the Least Common Multiple of 82500 and 82509?

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 82500 and 82509 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82500 and 82509, than apply into the LCM equation.

GCF(82500,82509) = 3
LCM(82500,82509) = ( 82500 × 82509) / 3
LCM(82500,82509) = 6806992500 / 3
LCM(82500,82509) = 2268997500

Least Common Multiple (LCM) of 82500 and 82509 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82500 and 82509. First we will calculate the prime factors of 82500 and 82509.

Prime Factorization of 82500

Prime Factorization of 82509

Now multiplying the highest exponent prime factors to calculate the LCM of 82500 and 82509.

LCM(82500,82509) = 2² × 3¹ × 5⁴ × 11¹ × 7¹ × 3929¹
LCM(82500,82509) = 2268997500