What is the Least Common Multiple of 14400 and 14415?

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 14400 and 14415 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14400 and 14415, than apply into the LCM equation.

GCF(14400,14415) = 15
LCM(14400,14415) = ( 14400 × 14415) / 15
LCM(14400,14415) = 207576000 / 15
LCM(14400,14415) = 13838400

Least Common Multiple (LCM) of 14400 and 14415 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14400 and 14415. First we will calculate the prime factors of 14400 and 14415.

Prime Factorization of 14400

Prime Factorization of 14415

Now multiplying the highest exponent prime factors to calculate the LCM of 14400 and 14415.

LCM(14400,14415) = 2⁶ × 3² × 5² × 31²
LCM(14400,14415) = 13838400