What is the Least Common Multiple of 14304 and 14319?

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 14304 and 14319 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14304 and 14319, than apply into the LCM equation.

GCF(14304,14319) = 3
LCM(14304,14319) = ( 14304 × 14319) / 3
LCM(14304,14319) = 204818976 / 3
LCM(14304,14319) = 68272992

Least Common Multiple (LCM) of 14304 and 14319 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14304 and 14319. First we will calculate the prime factors of 14304 and 14319.

Prime Factorization of 14304

Prime Factorization of 14319

Now multiplying the highest exponent prime factors to calculate the LCM of 14304 and 14319.

LCM(14304,14319) = 2⁵ × 3² × 149¹ × 37¹ × 43¹
LCM(14304,14319) = 68272992