What is the Least Common Multiple of 82800 and 82816?

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 82800 and 82816 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82800 and 82816, than apply into the LCM equation.

GCF(82800,82816) = 16
LCM(82800,82816) = ( 82800 × 82816) / 16
LCM(82800,82816) = 6857164800 / 16
LCM(82800,82816) = 428572800

Least Common Multiple (LCM) of 82800 and 82816 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82800 and 82816. First we will calculate the prime factors of 82800 and 82816.

Prime Factorization of 82800

Prime Factorization of 82816

Now multiplying the highest exponent prime factors to calculate the LCM of 82800 and 82816.

LCM(82800,82816) = 2⁷ × 3² × 5² × 23¹ × 647¹
LCM(82800,82816) = 428572800