What is the Least Common Multiple of 5586 and 5600?

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 5586 and 5600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5586 and 5600, than apply into the LCM equation.

GCF(5586,5600) = 14
LCM(5586,5600) = ( 5586 × 5600) / 14
LCM(5586,5600) = 31281600 / 14
LCM(5586,5600) = 2234400

Least Common Multiple (LCM) of 5586 and 5600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5586 and 5600. First we will calculate the prime factors of 5586 and 5600.

Prime Factorization of 5586

Prime Factorization of 5600

Now multiplying the highest exponent prime factors to calculate the LCM of 5586 and 5600.

LCM(5586,5600) = 2⁵ × 3¹ × 7² × 19¹ × 5²
LCM(5586,5600) = 2234400