What is the Least Common Multiple of 69586 and 69600?

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 69586 and 69600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69586 and 69600, than apply into the LCM equation.

GCF(69586,69600) = 2
LCM(69586,69600) = ( 69586 × 69600) / 2
LCM(69586,69600) = 4843185600 / 2
LCM(69586,69600) = 2421592800

Least Common Multiple (LCM) of 69586 and 69600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69586 and 69600. First we will calculate the prime factors of 69586 and 69600.

Prime Factorization of 69586

Prime Factorization of 69600

Now multiplying the highest exponent prime factors to calculate the LCM of 69586 and 69600.

LCM(69586,69600) = 2⁵ × 11¹ × 3163¹ × 3¹ × 5² × 29¹
LCM(69586,69600) = 2421592800