What is the Least Common Multiple of 31728 and 31734?

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 31734 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 31734, than apply into the LCM equation.

GCF(31728,31734) = 6
LCM(31728,31734) = ( 31728 × 31734) / 6
LCM(31728,31734) = 1006856352 / 6
LCM(31728,31734) = 167809392

Least Common Multiple (LCM) of 31728 and 31734 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31728 and 31734. First we will calculate the prime factors of 31728 and 31734.

Prime Factorization of 31728

Prime Factorization of 31734

Now multiplying the highest exponent prime factors to calculate the LCM of 31728 and 31734.

LCM(31728,31734) = 2⁴ × 3² × 661¹ × 41¹ × 43¹
LCM(31728,31734) = 167809392