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What is the Least Common Multiple of 9792 and 9812?

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 9812 is 24019776.

LCM(9792,9812) = 24019776

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Least Common Multiple of 9792 and 9812 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 9812, than apply into the LCM equation.

GCF(9792,9812) = 4
LCM(9792,9812) = ( 9792 × 9812) / 4
LCM(9792,9812) = 96079104 / 4
LCM(9792,9812) = 24019776

Least Common Multiple (LCM) of 9792 and 9812 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9792 and 9812. First we will calculate the prime factors of 9792 and 9812.

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 9812

Prime factors of 9812 are 2, 11, 223. Prime factorization of 9812 in exponential form is:

9812 = 22 × 111 × 2231

Now multiplying the highest exponent prime factors to calculate the LCM of 9792 and 9812.

LCM(9792,9812) = 26 × 32 × 171 × 111 × 2231
LCM(9792,9812) = 24019776