What is the Least Common Multiple of 22304 and 22320?

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 22320 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 22320, than apply into the LCM equation.

GCF(22304,22320) = 16
LCM(22304,22320) = ( 22304 × 22320) / 16
LCM(22304,22320) = 497825280 / 16
LCM(22304,22320) = 31114080

Least Common Multiple (LCM) of 22304 and 22320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 22304 and 22320. First we will calculate the prime factors of 22304 and 22320.

Prime Factorization of 22304

Prime Factorization of 22320

Now multiplying the highest exponent prime factors to calculate the LCM of 22304 and 22320.

LCM(22304,22320) = 2⁵ × 17¹ × 41¹ × 3² × 5¹ × 31¹
LCM(22304,22320) = 31114080