What is the Least Common Multiple of 12357 and 12375?

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 12357 and 12375 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12357 and 12375, than apply into the LCM equation.

GCF(12357,12375) = 9
LCM(12357,12375) = ( 12357 × 12375) / 9
LCM(12357,12375) = 152917875 / 9
LCM(12357,12375) = 16990875

Least Common Multiple (LCM) of 12357 and 12375 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12357 and 12375. First we will calculate the prime factors of 12357 and 12375.

Prime Factorization of 12357

Prime Factorization of 12375

Now multiplying the highest exponent prime factors to calculate the LCM of 12357 and 12375.

LCM(12357,12375) = 3² × 1373¹ × 5³ × 11¹
LCM(12357,12375) = 16990875