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What is the Least Common Multiple of 13704 and 13712?

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 13704 and 13712 is 23488656.

LCM(13704,13712) = 23488656

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Least Common Multiple of 13704 and 13712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13704 and 13712, than apply into the LCM equation.

GCF(13704,13712) = 8
LCM(13704,13712) = ( 13704 × 13712) / 8
LCM(13704,13712) = 187909248 / 8
LCM(13704,13712) = 23488656

Least Common Multiple (LCM) of 13704 and 13712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13704 and 13712. First we will calculate the prime factors of 13704 and 13712.

Prime Factorization of 13704

Prime factors of 13704 are 2, 3, 571. Prime factorization of 13704 in exponential form is:

13704 = 23 × 31 × 5711

Prime Factorization of 13712

Prime factors of 13712 are 2, 857. Prime factorization of 13712 in exponential form is:

13712 = 24 × 8571

Now multiplying the highest exponent prime factors to calculate the LCM of 13704 and 13712.

LCM(13704,13712) = 24 × 31 × 5711 × 8571
LCM(13704,13712) = 23488656