What is the Least Common Multiple of 31380 and 31400?

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 31380 and 31400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31380 and 31400, than apply into the LCM equation.

GCF(31380,31400) = 20
LCM(31380,31400) = ( 31380 × 31400) / 20
LCM(31380,31400) = 985332000 / 20
LCM(31380,31400) = 49266600

Least Common Multiple (LCM) of 31380 and 31400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31380 and 31400. First we will calculate the prime factors of 31380 and 31400.

Prime Factorization of 31380

Prime Factorization of 31400

Now multiplying the highest exponent prime factors to calculate the LCM of 31380 and 31400.

LCM(31380,31400) = 2³ × 3¹ × 5² × 523¹ × 157¹
LCM(31380,31400) = 49266600