What is the Least Common Multiple of 31900 and 31912?

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 31900 and 31912 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31900 and 31912, than apply into the LCM equation.

GCF(31900,31912) = 4
LCM(31900,31912) = ( 31900 × 31912) / 4
LCM(31900,31912) = 1017992800 / 4
LCM(31900,31912) = 254498200

Least Common Multiple (LCM) of 31900 and 31912 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31900 and 31912. First we will calculate the prime factors of 31900 and 31912.

Prime Factorization of 31900

Prime Factorization of 31912

Now multiplying the highest exponent prime factors to calculate the LCM of 31900 and 31912.

LCM(31900,31912) = 2³ × 5² × 11¹ × 29¹ × 3989¹
LCM(31900,31912) = 254498200