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What is the Least Common Multiple of 9792 and 9804?

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 9792 and 9804 is 8000064.

LCM(9792,9804) = 8000064

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Least Common Multiple of 9792 and 9804 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9792 and 9804, than apply into the LCM equation.

GCF(9792,9804) = 12
LCM(9792,9804) = ( 9792 × 9804) / 12
LCM(9792,9804) = 96000768 / 12
LCM(9792,9804) = 8000064

Least Common Multiple (LCM) of 9792 and 9804 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9792 and 9804. First we will calculate the prime factors of 9792 and 9804.

Prime Factorization of 9792

Prime factors of 9792 are 2, 3, 17. Prime factorization of 9792 in exponential form is:

9792 = 26 × 32 × 171

Prime Factorization of 9804

Prime factors of 9804 are 2, 3, 19, 43. Prime factorization of 9804 in exponential form is:

9804 = 22 × 31 × 191 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 9792 and 9804.

LCM(9792,9804) = 26 × 32 × 171 × 191 × 431
LCM(9792,9804) = 8000064