What is the Least Common Multiple of 31968 and 31974?

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 31974 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 31974, than apply into the LCM equation.

GCF(31968,31974) = 6
LCM(31968,31974) = ( 31968 × 31974) / 6
LCM(31968,31974) = 1022144832 / 6
LCM(31968,31974) = 170357472

Least Common Multiple (LCM) of 31968 and 31974 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31968 and 31974. First we will calculate the prime factors of 31968 and 31974.

Prime Factorization of 31968

Prime Factorization of 31974

Now multiplying the highest exponent prime factors to calculate the LCM of 31968 and 31974.

LCM(31968,31974) = 2⁵ × 3³ × 37¹ × 73²
LCM(31968,31974) = 170357472