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What is the Least Common Multiple of 10404 and 10412?

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 10404 and 10412 is 27081612.

LCM(10404,10412) = 27081612

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Least Common Multiple of 10404 and 10412 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10404 and 10412, than apply into the LCM equation.

GCF(10404,10412) = 4
LCM(10404,10412) = ( 10404 × 10412) / 4
LCM(10404,10412) = 108326448 / 4
LCM(10404,10412) = 27081612

Least Common Multiple (LCM) of 10404 and 10412 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10404 and 10412. First we will calculate the prime factors of 10404 and 10412.

Prime Factorization of 10404

Prime factors of 10404 are 2, 3, 17. Prime factorization of 10404 in exponential form is:

10404 = 22 × 32 × 172

Prime Factorization of 10412

Prime factors of 10412 are 2, 19, 137. Prime factorization of 10412 in exponential form is:

10412 = 22 × 191 × 1371

Now multiplying the highest exponent prime factors to calculate the LCM of 10404 and 10412.

LCM(10404,10412) = 22 × 32 × 172 × 191 × 1371
LCM(10404,10412) = 27081612