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What is the Least Common Multiple of 12304 and 12318?

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 12304 and 12318 is 75780336.

LCM(12304,12318) = 75780336

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Least Common Multiple of 12304 and 12318 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12304 and 12318, than apply into the LCM equation.

GCF(12304,12318) = 2
LCM(12304,12318) = ( 12304 × 12318) / 2
LCM(12304,12318) = 151560672 / 2
LCM(12304,12318) = 75780336

Least Common Multiple (LCM) of 12304 and 12318 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12304 and 12318. First we will calculate the prime factors of 12304 and 12318.

Prime Factorization of 12304

Prime factors of 12304 are 2, 769. Prime factorization of 12304 in exponential form is:

12304 = 24 × 7691

Prime Factorization of 12318

Prime factors of 12318 are 2, 3, 2053. Prime factorization of 12318 in exponential form is:

12318 = 21 × 31 × 20531

Now multiplying the highest exponent prime factors to calculate the LCM of 12304 and 12318.

LCM(12304,12318) = 24 × 7691 × 31 × 20531
LCM(12304,12318) = 75780336