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What is the Least Common Multiple of 10109 and 10122?

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 10109 and 10122 is 102323298.

LCM(10109,10122) = 102323298

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Least Common Multiple of 10109 and 10122 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10109 and 10122, than apply into the LCM equation.

GCF(10109,10122) = 1
LCM(10109,10122) = ( 10109 × 10122) / 1
LCM(10109,10122) = 102323298 / 1
LCM(10109,10122) = 102323298

Least Common Multiple (LCM) of 10109 and 10122 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10109 and 10122. First we will calculate the prime factors of 10109 and 10122.

Prime Factorization of 10109

Prime factors of 10109 are 11, 919. Prime factorization of 10109 in exponential form is:

10109 = 111 × 9191

Prime Factorization of 10122

Prime factors of 10122 are 2, 3, 7, 241. Prime factorization of 10122 in exponential form is:

10122 = 21 × 31 × 71 × 2411

Now multiplying the highest exponent prime factors to calculate the LCM of 10109 and 10122.

LCM(10109,10122) = 111 × 9191 × 21 × 31 × 71 × 2411
LCM(10109,10122) = 102323298