What is the Least Common Multiple of 31056 and 31072?

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 31072 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 31072, than apply into the LCM equation.

GCF(31056,31072) = 16
LCM(31056,31072) = ( 31056 × 31072) / 16
LCM(31056,31072) = 964972032 / 16
LCM(31056,31072) = 60310752

Least Common Multiple (LCM) of 31056 and 31072 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31056 and 31072. First we will calculate the prime factors of 31056 and 31072.

Prime Factorization of 31056

Prime Factorization of 31072

Now multiplying the highest exponent prime factors to calculate the LCM of 31056 and 31072.

LCM(31056,31072) = 2⁵ × 3¹ × 647¹ × 971¹
LCM(31056,31072) = 60310752