What is the Least Common Multiple of 31728 and 31746?

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 31728 and 31746 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31728 and 31746, than apply into the LCM equation.

GCF(31728,31746) = 6
LCM(31728,31746) = ( 31728 × 31746) / 6
LCM(31728,31746) = 1007237088 / 6
LCM(31728,31746) = 167872848

Least Common Multiple (LCM) of 31728 and 31746 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31728 and 31746. First we will calculate the prime factors of 31728 and 31746.

Prime Factorization of 31728

Prime Factorization of 31746

Now multiplying the highest exponent prime factors to calculate the LCM of 31728 and 31746.

LCM(31728,31746) = 2⁴ × 3¹ × 661¹ × 11¹ × 13¹ × 37¹
LCM(31728,31746) = 167872848