What is the Least Common Multiple of 12369 and 12384?

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 12369 and 12384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12369 and 12384, than apply into the LCM equation.

GCF(12369,12384) = 3
LCM(12369,12384) = ( 12369 × 12384) / 3
LCM(12369,12384) = 153177696 / 3
LCM(12369,12384) = 51059232

Least Common Multiple (LCM) of 12369 and 12384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12369 and 12384. First we will calculate the prime factors of 12369 and 12384.

Prime Factorization of 12369

Prime Factorization of 12384

Now multiplying the highest exponent prime factors to calculate the LCM of 12369 and 12384.

LCM(12369,12384) = 3² × 7¹ × 19¹ × 31¹ × 2⁵ × 43¹
LCM(12369,12384) = 51059232