What is the Least Common Multiple of 65584 and 65600?

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 65584 and 65600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65584 and 65600, than apply into the LCM equation.

GCF(65584,65600) = 16
LCM(65584,65600) = ( 65584 × 65600) / 16
LCM(65584,65600) = 4302310400 / 16
LCM(65584,65600) = 268894400

Least Common Multiple (LCM) of 65584 and 65600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65584 and 65600. First we will calculate the prime factors of 65584 and 65600.

Prime Factorization of 65584

Prime Factorization of 65600

Now multiplying the highest exponent prime factors to calculate the LCM of 65584 and 65600.

LCM(65584,65600) = 2⁶ × 4099¹ × 5² × 41¹
LCM(65584,65600) = 268894400