What is the Least Common Multiple of 82560 and 82575?

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 82560 and 82575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82560 and 82575, than apply into the LCM equation.

GCF(82560,82575) = 15
LCM(82560,82575) = ( 82560 × 82575) / 15
LCM(82560,82575) = 6817392000 / 15
LCM(82560,82575) = 454492800

Least Common Multiple (LCM) of 82560 and 82575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82560 and 82575. First we will calculate the prime factors of 82560 and 82575.

Prime Factorization of 82560

Prime Factorization of 82575

Now multiplying the highest exponent prime factors to calculate the LCM of 82560 and 82575.

LCM(82560,82575) = 2⁷ × 3² × 5² × 43¹ × 367¹
LCM(82560,82575) = 454492800