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What is the Least Common Multiple of 12297 and 12314?

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 12297 and 12314 is 151425258.

LCM(12297,12314) = 151425258

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Least Common Multiple of 12297 and 12314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12297 and 12314, than apply into the LCM equation.

GCF(12297,12314) = 1
LCM(12297,12314) = ( 12297 × 12314) / 1
LCM(12297,12314) = 151425258 / 1
LCM(12297,12314) = 151425258

Least Common Multiple (LCM) of 12297 and 12314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12297 and 12314. First we will calculate the prime factors of 12297 and 12314.

Prime Factorization of 12297

Prime factors of 12297 are 3, 4099. Prime factorization of 12297 in exponential form is:

12297 = 31 × 40991

Prime Factorization of 12314

Prime factors of 12314 are 2, 47, 131. Prime factorization of 12314 in exponential form is:

12314 = 21 × 471 × 1311

Now multiplying the highest exponent prime factors to calculate the LCM of 12297 and 12314.

LCM(12297,12314) = 31 × 40991 × 21 × 471 × 1311
LCM(12297,12314) = 151425258