What is the Least Common Multiple of 31584 and 31596?

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 31596 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 31596, than apply into the LCM equation.

GCF(31584,31596) = 12
LCM(31584,31596) = ( 31584 × 31596) / 12
LCM(31584,31596) = 997928064 / 12
LCM(31584,31596) = 83160672

Least Common Multiple (LCM) of 31584 and 31596 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31584 and 31596. First we will calculate the prime factors of 31584 and 31596.

Prime Factorization of 31584

Prime Factorization of 31596

Now multiplying the highest exponent prime factors to calculate the LCM of 31584 and 31596.

LCM(31584,31596) = 2⁵ × 3¹ × 7¹ × 47¹ × 2633¹
LCM(31584,31596) = 83160672