What is the Least Common Multiple of 31968 and 31982?

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 31968 and 31982 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31968 and 31982, than apply into the LCM equation.

GCF(31968,31982) = 2
LCM(31968,31982) = ( 31968 × 31982) / 2
LCM(31968,31982) = 1022400576 / 2
LCM(31968,31982) = 511200288

Least Common Multiple (LCM) of 31968 and 31982 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31968 and 31982. First we will calculate the prime factors of 31968 and 31982.

Prime Factorization of 31968

Prime Factorization of 31982

Now multiplying the highest exponent prime factors to calculate the LCM of 31968 and 31982.

LCM(31968,31982) = 2⁵ × 3³ × 37¹ × 15991¹
LCM(31968,31982) = 511200288