What is the Least Common Multiple of 19584 and 19593?

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 19584 and 19593 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19584 and 19593, than apply into the LCM equation.

GCF(19584,19593) = 9
LCM(19584,19593) = ( 19584 × 19593) / 9
LCM(19584,19593) = 383709312 / 9
LCM(19584,19593) = 42634368

Least Common Multiple (LCM) of 19584 and 19593 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19584 and 19593. First we will calculate the prime factors of 19584 and 19593.

Prime Factorization of 19584

Prime Factorization of 19593

Now multiplying the highest exponent prime factors to calculate the LCM of 19584 and 19593.

LCM(19584,19593) = 2⁷ × 3² × 17¹ × 7¹ × 311¹
LCM(19584,19593) = 42634368