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What is the Least Common Multiple of 10105 and 10117?

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 10105 and 10117 is 102232285.

LCM(10105,10117) = 102232285

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Least Common Multiple of 10105 and 10117 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10105 and 10117, than apply into the LCM equation.

GCF(10105,10117) = 1
LCM(10105,10117) = ( 10105 × 10117) / 1
LCM(10105,10117) = 102232285 / 1
LCM(10105,10117) = 102232285

Least Common Multiple (LCM) of 10105 and 10117 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10105 and 10117. First we will calculate the prime factors of 10105 and 10117.

Prime Factorization of 10105

Prime factors of 10105 are 5, 43, 47. Prime factorization of 10105 in exponential form is:

10105 = 51 × 431 × 471

Prime Factorization of 10117

Prime factors of 10117 are 67, 151. Prime factorization of 10117 in exponential form is:

10117 = 671 × 1511

Now multiplying the highest exponent prime factors to calculate the LCM of 10105 and 10117.

LCM(10105,10117) = 51 × 431 × 471 × 671 × 1511
LCM(10105,10117) = 102232285