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What is the Least Common Multiple of 12704 and 12712?

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 12704 and 12712 is 20186656.

LCM(12704,12712) = 20186656

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Least Common Multiple of 12704 and 12712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12704 and 12712, than apply into the LCM equation.

GCF(12704,12712) = 8
LCM(12704,12712) = ( 12704 × 12712) / 8
LCM(12704,12712) = 161493248 / 8
LCM(12704,12712) = 20186656

Least Common Multiple (LCM) of 12704 and 12712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12704 and 12712. First we will calculate the prime factors of 12704 and 12712.

Prime Factorization of 12704

Prime factors of 12704 are 2, 397. Prime factorization of 12704 in exponential form is:

12704 = 25 × 3971

Prime Factorization of 12712

Prime factors of 12712 are 2, 7, 227. Prime factorization of 12712 in exponential form is:

12712 = 23 × 71 × 2271

Now multiplying the highest exponent prime factors to calculate the LCM of 12704 and 12712.

LCM(12704,12712) = 25 × 3971 × 71 × 2271
LCM(12704,12712) = 20186656