What is the Least Common Multiple of 31260 and 31275?

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 31260 and 31275 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31260 and 31275, than apply into the LCM equation.

GCF(31260,31275) = 15
LCM(31260,31275) = ( 31260 × 31275) / 15
LCM(31260,31275) = 977656500 / 15
LCM(31260,31275) = 65177100

Least Common Multiple (LCM) of 31260 and 31275 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31260 and 31275. First we will calculate the prime factors of 31260 and 31275.

Prime Factorization of 31260

Prime Factorization of 31275

Now multiplying the highest exponent prime factors to calculate the LCM of 31260 and 31275.

LCM(31260,31275) = 2² × 3² × 5² × 521¹ × 139¹
LCM(31260,31275) = 65177100