What is the Least Common Multiple of 31584 and 31591?

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 31584 and 31591 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31584 and 31591, than apply into the LCM equation.

GCF(31584,31591) = 7
LCM(31584,31591) = ( 31584 × 31591) / 7
LCM(31584,31591) = 997770144 / 7
LCM(31584,31591) = 142538592

Least Common Multiple (LCM) of 31584 and 31591 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31584 and 31591. First we will calculate the prime factors of 31584 and 31591.

Prime Factorization of 31584

Prime Factorization of 31591

Now multiplying the highest exponent prime factors to calculate the LCM of 31584 and 31591.

LCM(31584,31591) = 2⁵ × 3¹ × 7¹ × 47¹ × 4513¹
LCM(31584,31591) = 142538592