What is the Least Common Multiple of 85344 and 85359?

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 85344 and 85359 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85344 and 85359, than apply into the LCM equation.

GCF(85344,85359) = 3
LCM(85344,85359) = ( 85344 × 85359) / 3
LCM(85344,85359) = 7284878496 / 3
LCM(85344,85359) = 2428292832

Least Common Multiple (LCM) of 85344 and 85359 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85344 and 85359. First we will calculate the prime factors of 85344 and 85359.

Prime Factorization of 85344

Prime Factorization of 85359

Now multiplying the highest exponent prime factors to calculate the LCM of 85344 and 85359.

LCM(85344,85359) = 2⁵ × 3¹ × 7¹ × 127¹ × 37¹ × 769¹
LCM(85344,85359) = 2428292832