What is the Least Common Multiple of 22304 and 22314?

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 22304 and 22314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 22304 and 22314, than apply into the LCM equation.

GCF(22304,22314) = 2
LCM(22304,22314) = ( 22304 × 22314) / 2
LCM(22304,22314) = 497691456 / 2
LCM(22304,22314) = 248845728

Least Common Multiple (LCM) of 22304 and 22314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 22304 and 22314. First we will calculate the prime factors of 22304 and 22314.

Prime Factorization of 22304

Prime Factorization of 22314

Now multiplying the highest exponent prime factors to calculate the LCM of 22304 and 22314.

LCM(22304,22314) = 2⁵ × 17¹ × 41¹ × 3¹ × 3719¹
LCM(22304,22314) = 248845728