What is the Least Common Multiple of 38304 and 38322?

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 38304 and 38322 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38304 and 38322, than apply into the LCM equation.

GCF(38304,38322) = 18
LCM(38304,38322) = ( 38304 × 38322) / 18
LCM(38304,38322) = 1467885888 / 18
LCM(38304,38322) = 81549216

Least Common Multiple (LCM) of 38304 and 38322 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38304 and 38322. First we will calculate the prime factors of 38304 and 38322.

Prime Factorization of 38304

Prime Factorization of 38322

Now multiplying the highest exponent prime factors to calculate the LCM of 38304 and 38322.

LCM(38304,38322) = 2⁵ × 3² × 7¹ × 19¹ × 2129¹
LCM(38304,38322) = 81549216