What is the Least Common Multiple of 67584 and 67600?

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 67600 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 67600, than apply into the LCM equation.

GCF(67584,67600) = 16
LCM(67584,67600) = ( 67584 × 67600) / 16
LCM(67584,67600) = 4568678400 / 16
LCM(67584,67600) = 285542400

Least Common Multiple (LCM) of 67584 and 67600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67584 and 67600. First we will calculate the prime factors of 67584 and 67600.

Prime Factorization of 67584

Prime Factorization of 67600

Now multiplying the highest exponent prime factors to calculate the LCM of 67584 and 67600.

LCM(67584,67600) = 2¹¹ × 3¹ × 11¹ × 5² × 13²
LCM(67584,67600) = 285542400