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What is the Least Common Multiple of 6312 and 6321?

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 6312 and 6321 is 13299384.

LCM(6312,6321) = 13299384

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Least Common Multiple of 6312 and 6321 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6312 and 6321, than apply into the LCM equation.

GCF(6312,6321) = 3
LCM(6312,6321) = ( 6312 × 6321) / 3
LCM(6312,6321) = 39898152 / 3
LCM(6312,6321) = 13299384

Least Common Multiple (LCM) of 6312 and 6321 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6312 and 6321. First we will calculate the prime factors of 6312 and 6321.

Prime Factorization of 6312

Prime factors of 6312 are 2, 3, 263. Prime factorization of 6312 in exponential form is:

6312 = 23 × 31 × 2631

Prime Factorization of 6321

Prime factors of 6321 are 3, 7, 43. Prime factorization of 6321 in exponential form is:

6321 = 31 × 72 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 6312 and 6321.

LCM(6312,6321) = 23 × 31 × 2631 × 72 × 431
LCM(6312,6321) = 13299384