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What is the Least Common Multiple of 6315 and 6324?

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 6315 and 6324 is 13312020.

LCM(6315,6324) = 13312020

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Least Common Multiple of 6315 and 6324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6315 and 6324, than apply into the LCM equation.

GCF(6315,6324) = 3
LCM(6315,6324) = ( 6315 × 6324) / 3
LCM(6315,6324) = 39936060 / 3
LCM(6315,6324) = 13312020

Least Common Multiple (LCM) of 6315 and 6324 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6315 and 6324. First we will calculate the prime factors of 6315 and 6324.

Prime Factorization of 6315

Prime factors of 6315 are 3, 5, 421. Prime factorization of 6315 in exponential form is:

6315 = 31 × 51 × 4211

Prime Factorization of 6324

Prime factors of 6324 are 2, 3, 17, 31. Prime factorization of 6324 in exponential form is:

6324 = 22 × 31 × 171 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 6315 and 6324.

LCM(6315,6324) = 31 × 51 × 4211 × 22 × 171 × 311
LCM(6315,6324) = 13312020