What is the Least Common Multiple of 31700 and 31707?

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 31700 and 31707 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31700 and 31707, than apply into the LCM equation.

GCF(31700,31707) = 1
LCM(31700,31707) = ( 31700 × 31707) / 1
LCM(31700,31707) = 1005111900 / 1
LCM(31700,31707) = 1005111900

Least Common Multiple (LCM) of 31700 and 31707 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31700 and 31707. First we will calculate the prime factors of 31700 and 31707.

Prime Factorization of 31700

Prime Factorization of 31707

Now multiplying the highest exponent prime factors to calculate the LCM of 31700 and 31707.

LCM(31700,31707) = 2² × 5² × 317¹ × 3² × 13¹ × 271¹
LCM(31700,31707) = 1005111900