What is the Least Common Multiple of 11586 and 11600?

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 11586 and 11600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 11586 and 11600, than apply into the LCM equation.

GCF(11586,11600) = 2
LCM(11586,11600) = ( 11586 × 11600) / 2
LCM(11586,11600) = 134397600 / 2
LCM(11586,11600) = 67198800

Least Common Multiple (LCM) of 11586 and 11600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 11586 and 11600. First we will calculate the prime factors of 11586 and 11600.

Prime Factorization of 11586

Prime Factorization of 11600

Now multiplying the highest exponent prime factors to calculate the LCM of 11586 and 11600.

LCM(11586,11600) = 2⁴ × 3¹ × 1931¹ × 5² × 29¹
LCM(11586,11600) = 67198800