What is the Least Common Multiple of 82400 and 82415?

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 82400 and 82415 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82400 and 82415, than apply into the LCM equation.

GCF(82400,82415) = 5
LCM(82400,82415) = ( 82400 × 82415) / 5
LCM(82400,82415) = 6790996000 / 5
LCM(82400,82415) = 1358199200

Least Common Multiple (LCM) of 82400 and 82415 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82400 and 82415. First we will calculate the prime factors of 82400 and 82415.

Prime Factorization of 82400

Prime Factorization of 82415

Now multiplying the highest exponent prime factors to calculate the LCM of 82400 and 82415.

LCM(82400,82415) = 2⁵ × 5² × 103¹ × 53¹ × 311¹
LCM(82400,82415) = 1358199200