What is the Least Common Multiple of 31875 and 31880?

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 31875 and 31880 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31875 and 31880, than apply into the LCM equation.

GCF(31875,31880) = 5
LCM(31875,31880) = ( 31875 × 31880) / 5
LCM(31875,31880) = 1016175000 / 5
LCM(31875,31880) = 203235000

Least Common Multiple (LCM) of 31875 and 31880 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31875 and 31880. First we will calculate the prime factors of 31875 and 31880.

Prime Factorization of 31875

Prime Factorization of 31880

Now multiplying the highest exponent prime factors to calculate the LCM of 31875 and 31880.

LCM(31875,31880) = 3¹ × 5⁴ × 17¹ × 2³ × 797¹
LCM(31875,31880) = 203235000