What is the Least Common Multiple of 12306 and 12314?

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 12306 and 12314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12306 and 12314, than apply into the LCM equation.

GCF(12306,12314) = 2
LCM(12306,12314) = ( 12306 × 12314) / 2
LCM(12306,12314) = 151536084 / 2
LCM(12306,12314) = 75768042

Least Common Multiple (LCM) of 12306 and 12314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12306 and 12314. First we will calculate the prime factors of 12306 and 12314.

Prime Factorization of 12306

Prime Factorization of 12314

Now multiplying the highest exponent prime factors to calculate the LCM of 12306 and 12314.

LCM(12306,12314) = 2¹ × 3¹ × 7¹ × 293¹ × 47¹ × 131¹
LCM(12306,12314) = 75768042