What is the Least Common Multiple of 31700 and 31714?

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 31714 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 31714, than apply into the LCM equation.

GCF(31700,31714) = 2
LCM(31700,31714) = ( 31700 × 31714) / 2
LCM(31700,31714) = 1005333800 / 2
LCM(31700,31714) = 502666900

Least Common Multiple (LCM) of 31700 and 31714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31700 and 31714. First we will calculate the prime factors of 31700 and 31714.

Prime Factorization of 31700

Prime Factorization of 31714

Now multiplying the highest exponent prime factors to calculate the LCM of 31700 and 31714.

LCM(31700,31714) = 2² × 5² × 317¹ × 101¹ × 157¹
LCM(31700,31714) = 502666900