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What is the Least Common Multiple of 12576 and 12592?

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 12576 and 12592 is 9897312.

LCM(12576,12592) = 9897312

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Least Common Multiple of 12576 and 12592 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12576 and 12592, than apply into the LCM equation.

GCF(12576,12592) = 16
LCM(12576,12592) = ( 12576 × 12592) / 16
LCM(12576,12592) = 158356992 / 16
LCM(12576,12592) = 9897312

Least Common Multiple (LCM) of 12576 and 12592 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12576 and 12592. First we will calculate the prime factors of 12576 and 12592.

Prime Factorization of 12576

Prime factors of 12576 are 2, 3, 131. Prime factorization of 12576 in exponential form is:

12576 = 25 × 31 × 1311

Prime Factorization of 12592

Prime factors of 12592 are 2, 787. Prime factorization of 12592 in exponential form is:

12592 = 24 × 7871

Now multiplying the highest exponent prime factors to calculate the LCM of 12576 and 12592.

LCM(12576,12592) = 25 × 31 × 1311 × 7871
LCM(12576,12592) = 9897312