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What is the Least Common Multiple of 10306 and 10317?

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 10306 and 10317 is 106327002.

LCM(10306,10317) = 106327002

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Least Common Multiple of 10306 and 10317 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10306 and 10317, than apply into the LCM equation.

GCF(10306,10317) = 1
LCM(10306,10317) = ( 10306 × 10317) / 1
LCM(10306,10317) = 106327002 / 1
LCM(10306,10317) = 106327002

Least Common Multiple (LCM) of 10306 and 10317 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10306 and 10317. First we will calculate the prime factors of 10306 and 10317.

Prime Factorization of 10306

Prime factors of 10306 are 2, 5153. Prime factorization of 10306 in exponential form is:

10306 = 21 × 51531

Prime Factorization of 10317

Prime factors of 10317 are 3, 19, 181. Prime factorization of 10317 in exponential form is:

10317 = 31 × 191 × 1811

Now multiplying the highest exponent prime factors to calculate the LCM of 10306 and 10317.

LCM(10306,10317) = 21 × 51531 × 31 × 191 × 1811
LCM(10306,10317) = 106327002