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What is the Least Common Multiple of 12596 and 12608?

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 12596 and 12608 is 39702592.

LCM(12596,12608) = 39702592

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Least Common Multiple of 12596 and 12608 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12596 and 12608, than apply into the LCM equation.

GCF(12596,12608) = 4
LCM(12596,12608) = ( 12596 × 12608) / 4
LCM(12596,12608) = 158810368 / 4
LCM(12596,12608) = 39702592

Least Common Multiple (LCM) of 12596 and 12608 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12596 and 12608. First we will calculate the prime factors of 12596 and 12608.

Prime Factorization of 12596

Prime factors of 12596 are 2, 47, 67. Prime factorization of 12596 in exponential form is:

12596 = 22 × 471 × 671

Prime Factorization of 12608

Prime factors of 12608 are 2, 197. Prime factorization of 12608 in exponential form is:

12608 = 26 × 1971

Now multiplying the highest exponent prime factors to calculate the LCM of 12596 and 12608.

LCM(12596,12608) = 26 × 471 × 671 × 1971
LCM(12596,12608) = 39702592