What is the Least Common Multiple of 12336 and 12345?

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 12336 and 12345 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12336 and 12345, than apply into the LCM equation.

GCF(12336,12345) = 3
LCM(12336,12345) = ( 12336 × 12345) / 3
LCM(12336,12345) = 152287920 / 3
LCM(12336,12345) = 50762640

Least Common Multiple (LCM) of 12336 and 12345 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12336 and 12345. First we will calculate the prime factors of 12336 and 12345.

Prime Factorization of 12336

Prime Factorization of 12345

Now multiplying the highest exponent prime factors to calculate the LCM of 12336 and 12345.

LCM(12336,12345) = 2⁴ × 3¹ × 257¹ × 5¹ × 823¹
LCM(12336,12345) = 50762640