What is the Least Common Multiple of 31709 and 31728?

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 31709 and 31728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31709 and 31728, than apply into the LCM equation.

GCF(31709,31728) = 1
LCM(31709,31728) = ( 31709 × 31728) / 1
LCM(31709,31728) = 1006063152 / 1
LCM(31709,31728) = 1006063152

Least Common Multiple (LCM) of 31709 and 31728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31709 and 31728. First we will calculate the prime factors of 31709 and 31728.

Prime Factorization of 31709

Prime Factorization of 31728

Now multiplying the highest exponent prime factors to calculate the LCM of 31709 and 31728.

LCM(31709,31728) = 37¹ × 857¹ × 2⁴ × 3¹ × 661¹
LCM(31709,31728) = 1006063152