What is the Least Common Multiple of 31680 and 31700?

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 31680 and 31700 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31680 and 31700, than apply into the LCM equation.

GCF(31680,31700) = 20
LCM(31680,31700) = ( 31680 × 31700) / 20
LCM(31680,31700) = 1004256000 / 20
LCM(31680,31700) = 50212800

Least Common Multiple (LCM) of 31680 and 31700 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31680 and 31700. First we will calculate the prime factors of 31680 and 31700.

Prime Factorization of 31680

Prime Factorization of 31700

Now multiplying the highest exponent prime factors to calculate the LCM of 31680 and 31700.

LCM(31680,31700) = 2⁶ × 3² × 5² × 11¹ × 317¹
LCM(31680,31700) = 50212800