What is the Least Common Multiple of 31056 and 31074?

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 31056 and 31074 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31056 and 31074, than apply into the LCM equation.

GCF(31056,31074) = 6
LCM(31056,31074) = ( 31056 × 31074) / 6
LCM(31056,31074) = 965034144 / 6
LCM(31056,31074) = 160839024

Least Common Multiple (LCM) of 31056 and 31074 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31056 and 31074. First we will calculate the prime factors of 31056 and 31074.

Prime Factorization of 31056

Prime Factorization of 31074

Now multiplying the highest exponent prime factors to calculate the LCM of 31056 and 31074.

LCM(31056,31074) = 2⁴ × 3¹ × 647¹ × 5179¹
LCM(31056,31074) = 160839024