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What is the Least Common Multiple of 10096 and 10114?

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 10096 and 10114 is 51055472.

LCM(10096,10114) = 51055472

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Least Common Multiple of 10096 and 10114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10096 and 10114, than apply into the LCM equation.

GCF(10096,10114) = 2
LCM(10096,10114) = ( 10096 × 10114) / 2
LCM(10096,10114) = 102110944 / 2
LCM(10096,10114) = 51055472

Least Common Multiple (LCM) of 10096 and 10114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10096 and 10114. First we will calculate the prime factors of 10096 and 10114.

Prime Factorization of 10096

Prime factors of 10096 are 2, 631. Prime factorization of 10096 in exponential form is:

10096 = 24 × 6311

Prime Factorization of 10114

Prime factors of 10114 are 2, 13, 389. Prime factorization of 10114 in exponential form is:

10114 = 21 × 131 × 3891

Now multiplying the highest exponent prime factors to calculate the LCM of 10096 and 10114.

LCM(10096,10114) = 24 × 6311 × 131 × 3891
LCM(10096,10114) = 51055472