What is the Least Common Multiple of 12300 and 12312?

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 12300 and 12312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12300 and 12312, than apply into the LCM equation.

GCF(12300,12312) = 12
LCM(12300,12312) = ( 12300 × 12312) / 12
LCM(12300,12312) = 151437600 / 12
LCM(12300,12312) = 12619800

Least Common Multiple (LCM) of 12300 and 12312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12300 and 12312. First we will calculate the prime factors of 12300 and 12312.

Prime Factorization of 12300

Prime Factorization of 12312

Now multiplying the highest exponent prime factors to calculate the LCM of 12300 and 12312.

LCM(12300,12312) = 2³ × 3⁴ × 5² × 41¹ × 19¹
LCM(12300,12312) = 12619800