What is the Least Common Multiple of 82395 and 82400?

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 82395 and 82400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82395 and 82400, than apply into the LCM equation.

GCF(82395,82400) = 5
LCM(82395,82400) = ( 82395 × 82400) / 5
LCM(82395,82400) = 6789348000 / 5
LCM(82395,82400) = 1357869600

Least Common Multiple (LCM) of 82395 and 82400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82395 and 82400. First we will calculate the prime factors of 82395 and 82400.

Prime Factorization of 82395

Prime Factorization of 82400

Now multiplying the highest exponent prime factors to calculate the LCM of 82395 and 82400.

LCM(82395,82400) = 3² × 5² × 1831¹ × 2⁵ × 103¹
LCM(82395,82400) = 1357869600