What is the Least Common Multiple of 6304 and 6314?

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 6304 and 6314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6304 and 6314, than apply into the LCM equation.

GCF(6304,6314) = 2
LCM(6304,6314) = ( 6304 × 6314) / 2
LCM(6304,6314) = 39803456 / 2
LCM(6304,6314) = 19901728

Least Common Multiple (LCM) of 6304 and 6314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6304 and 6314. First we will calculate the prime factors of 6304 and 6314.

Prime Factorization of 6304

Prime Factorization of 6314

Now multiplying the highest exponent prime factors to calculate the LCM of 6304 and 6314.

LCM(6304,6314) = 2⁵ × 197¹ × 7¹ × 11¹ × 41¹
LCM(6304,6314) = 19901728