What is the Least Common Multiple of 67584 and 67599?

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 67584 and 67599 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67584 and 67599, than apply into the LCM equation.

GCF(67584,67599) = 3
LCM(67584,67599) = ( 67584 × 67599) / 3
LCM(67584,67599) = 4568610816 / 3
LCM(67584,67599) = 1522870272

Least Common Multiple (LCM) of 67584 and 67599 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67584 and 67599. First we will calculate the prime factors of 67584 and 67599.

Prime Factorization of 67584

Prime Factorization of 67599

Now multiplying the highest exponent prime factors to calculate the LCM of 67584 and 67599.

LCM(67584,67599) = 2¹¹ × 3² × 11¹ × 7¹ × 29¹ × 37¹
LCM(67584,67599) = 1522870272