What is the Least Common Multiple of 9588 and 9600?

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 9588 and 9600 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9588 and 9600, than apply into the LCM equation.

GCF(9588,9600) = 12
LCM(9588,9600) = ( 9588 × 9600) / 12
LCM(9588,9600) = 92044800 / 12
LCM(9588,9600) = 7670400

Least Common Multiple (LCM) of 9588 and 9600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9588 and 9600. First we will calculate the prime factors of 9588 and 9600.

Prime Factorization of 9588

Prime Factorization of 9600

Now multiplying the highest exponent prime factors to calculate the LCM of 9588 and 9600.

LCM(9588,9600) = 2⁷ × 3¹ × 17¹ × 47¹ × 5²
LCM(9588,9600) = 7670400