What is the Least Common Multiple of 12300 and 12306?

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 12306 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 12306, than apply into the LCM equation.

GCF(12300,12306) = 6
LCM(12300,12306) = ( 12300 × 12306) / 6
LCM(12300,12306) = 151363800 / 6
LCM(12300,12306) = 25227300

Least Common Multiple (LCM) of 12300 and 12306 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12300 and 12306. First we will calculate the prime factors of 12300 and 12306.

Prime Factorization of 12300

Prime Factorization of 12306

Now multiplying the highest exponent prime factors to calculate the LCM of 12300 and 12306.

LCM(12300,12306) = 2² × 3¹ × 5² × 41¹ × 7¹ × 293¹
LCM(12300,12306) = 25227300