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What is the Least Common Multiple of 9712 and 9728?

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 9712 and 9728 is 5904896.

LCM(9712,9728) = 5904896

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Least Common Multiple of 9712 and 9728 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9712 and 9728, than apply into the LCM equation.

GCF(9712,9728) = 16
LCM(9712,9728) = ( 9712 × 9728) / 16
LCM(9712,9728) = 94478336 / 16
LCM(9712,9728) = 5904896

Least Common Multiple (LCM) of 9712 and 9728 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9712 and 9728. First we will calculate the prime factors of 9712 and 9728.

Prime Factorization of 9712

Prime factors of 9712 are 2, 607. Prime factorization of 9712 in exponential form is:

9712 = 24 × 6071

Prime Factorization of 9728

Prime factors of 9728 are 2, 19. Prime factorization of 9728 in exponential form is:

9728 = 29 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 9712 and 9728.

LCM(9712,9728) = 29 × 6071 × 191
LCM(9712,9728) = 5904896