What is the Least Common Multiple of 31480 and 31500?

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 31480 and 31500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31480 and 31500, than apply into the LCM equation.

GCF(31480,31500) = 20
LCM(31480,31500) = ( 31480 × 31500) / 20
LCM(31480,31500) = 991620000 / 20
LCM(31480,31500) = 49581000

Least Common Multiple (LCM) of 31480 and 31500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31480 and 31500. First we will calculate the prime factors of 31480 and 31500.

Prime Factorization of 31480

Prime Factorization of 31500

Now multiplying the highest exponent prime factors to calculate the LCM of 31480 and 31500.

LCM(31480,31500) = 2³ × 5³ × 787¹ × 3² × 7¹
LCM(31480,31500) = 49581000