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What is the Least Common Multiple of 10299 and 10312?

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 10299 and 10312 is 106203288.

LCM(10299,10312) = 106203288

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Least Common Multiple of 10299 and 10312 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10299 and 10312, than apply into the LCM equation.

GCF(10299,10312) = 1
LCM(10299,10312) = ( 10299 × 10312) / 1
LCM(10299,10312) = 106203288 / 1
LCM(10299,10312) = 106203288

Least Common Multiple (LCM) of 10299 and 10312 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10299 and 10312. First we will calculate the prime factors of 10299 and 10312.

Prime Factorization of 10299

Prime factors of 10299 are 3, 3433. Prime factorization of 10299 in exponential form is:

10299 = 31 × 34331

Prime Factorization of 10312

Prime factors of 10312 are 2, 1289. Prime factorization of 10312 in exponential form is:

10312 = 23 × 12891

Now multiplying the highest exponent prime factors to calculate the LCM of 10299 and 10312.

LCM(10299,10312) = 31 × 34331 × 23 × 12891
LCM(10299,10312) = 106203288