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What is the Least Common Multiple of 9584 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 (LCM) of 9584 and 9600 is 5750400.

LCM(9584,9600) = 5750400

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Least Common Multiple of 9584 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 9584 and 9600, than apply into the LCM equation.

GCF(9584,9600) = 16
LCM(9584,9600) = ( 9584 × 9600) / 16
LCM(9584,9600) = 92006400 / 16
LCM(9584,9600) = 5750400

Least Common Multiple (LCM) of 9584 and 9600 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9584 and 9600. First we will calculate the prime factors of 9584 and 9600.

Prime Factorization of 9584

Prime factors of 9584 are 2, 599. Prime factorization of 9584 in exponential form is:

9584 = 24 × 5991

Prime Factorization of 9600

Prime factors of 9600 are 2, 3, 5. Prime factorization of 9600 in exponential form is:

9600 = 27 × 31 × 52

Now multiplying the highest exponent prime factors to calculate the LCM of 9584 and 9600.

LCM(9584,9600) = 27 × 5991 × 31 × 52
LCM(9584,9600) = 5750400