What is the Least Common Multiple of 82500 and 82519?

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 82519 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 82519, than apply into the LCM equation.

GCF(82500,82519) = 1
LCM(82500,82519) = ( 82500 × 82519) / 1
LCM(82500,82519) = 6807817500 / 1
LCM(82500,82519) = 6807817500

Least Common Multiple (LCM) of 82500 and 82519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82500 and 82519. First we will calculate the prime factors of 82500 and 82519.

Prime Factorization of 82500

Prime Factorization of 82519

Now multiplying the highest exponent prime factors to calculate the LCM of 82500 and 82519.

LCM(82500,82519) = 2² × 3¹ × 5⁴ × 11¹ × 179¹ × 461¹
LCM(82500,82519) = 6807817500