What is the Least Common Multiple of 31860 and 31875?

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 31860 and 31875 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31860 and 31875, than apply into the LCM equation.

GCF(31860,31875) = 15
LCM(31860,31875) = ( 31860 × 31875) / 15
LCM(31860,31875) = 1015537500 / 15
LCM(31860,31875) = 67702500

Least Common Multiple (LCM) of 31860 and 31875 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31860 and 31875. First we will calculate the prime factors of 31860 and 31875.

Prime Factorization of 31860

Prime Factorization of 31875

Now multiplying the highest exponent prime factors to calculate the LCM of 31860 and 31875.

LCM(31860,31875) = 2² × 3³ × 5⁴ × 59¹ × 17¹
LCM(31860,31875) = 67702500