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What is the Least Common Multiple of 6306 and 6314?

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 6306 and 6314 is 19908042.

LCM(6306,6314) = 19908042

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Least Common Multiple of 6306 and 6314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6306 and 6314, than apply into the LCM equation.

GCF(6306,6314) = 2
LCM(6306,6314) = ( 6306 × 6314) / 2
LCM(6306,6314) = 39816084 / 2
LCM(6306,6314) = 19908042

Least Common Multiple (LCM) of 6306 and 6314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6306 and 6314. First we will calculate the prime factors of 6306 and 6314.

Prime Factorization of 6306

Prime factors of 6306 are 2, 3, 1051. Prime factorization of 6306 in exponential form is:

6306 = 21 × 31 × 10511

Prime Factorization of 6314

Prime factors of 6314 are 2, 7, 11, 41. Prime factorization of 6314 in exponential form is:

6314 = 21 × 71 × 111 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 6306 and 6314.

LCM(6306,6314) = 21 × 31 × 10511 × 71 × 111 × 411
LCM(6306,6314) = 19908042