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What is the Least Common Multiple of 9708 and 9724?

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 9708 and 9724 is 23600148.

LCM(9708,9724) = 23600148

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Least Common Multiple of 9708 and 9724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9708 and 9724, than apply into the LCM equation.

GCF(9708,9724) = 4
LCM(9708,9724) = ( 9708 × 9724) / 4
LCM(9708,9724) = 94400592 / 4
LCM(9708,9724) = 23600148

Least Common Multiple (LCM) of 9708 and 9724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9708 and 9724. First we will calculate the prime factors of 9708 and 9724.

Prime Factorization of 9708

Prime factors of 9708 are 2, 3, 809. Prime factorization of 9708 in exponential form is:

9708 = 22 × 31 × 8091

Prime Factorization of 9724

Prime factors of 9724 are 2, 11, 13, 17. Prime factorization of 9724 in exponential form is:

9724 = 22 × 111 × 131 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 9708 and 9724.

LCM(9708,9724) = 22 × 31 × 8091 × 111 × 131 × 171
LCM(9708,9724) = 23600148