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What is the Least Common Multiple of 12364 and 12384?

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 12364 and 12384 is 38278944.

LCM(12364,12384) = 38278944

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Least Common Multiple of 12364 and 12384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12364 and 12384, than apply into the LCM equation.

GCF(12364,12384) = 4
LCM(12364,12384) = ( 12364 × 12384) / 4
LCM(12364,12384) = 153115776 / 4
LCM(12364,12384) = 38278944

Least Common Multiple (LCM) of 12364 and 12384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12364 and 12384. First we will calculate the prime factors of 12364 and 12384.

Prime Factorization of 12364

Prime factors of 12364 are 2, 11, 281. Prime factorization of 12364 in exponential form is:

12364 = 22 × 111 × 2811

Prime Factorization of 12384

Prime factors of 12384 are 2, 3, 43. Prime factorization of 12384 in exponential form is:

12384 = 25 × 32 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 12364 and 12384.

LCM(12364,12384) = 25 × 111 × 2811 × 32 × 431
LCM(12364,12384) = 38278944