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What is the Least Common Multiple of 12302 and 12306?

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 12302 and 12306 is 75694206.

LCM(12302,12306) = 75694206

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Least Common Multiple of 12302 and 12306 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12302 and 12306, than apply into the LCM equation.

GCF(12302,12306) = 2
LCM(12302,12306) = ( 12302 × 12306) / 2
LCM(12302,12306) = 151388412 / 2
LCM(12302,12306) = 75694206

Least Common Multiple (LCM) of 12302 and 12306 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12302 and 12306. First we will calculate the prime factors of 12302 and 12306.

Prime Factorization of 12302

Prime factors of 12302 are 2, 6151. Prime factorization of 12302 in exponential form is:

12302 = 21 × 61511

Prime Factorization of 12306

Prime factors of 12306 are 2, 3, 7, 293. Prime factorization of 12306 in exponential form is:

12306 = 21 × 31 × 71 × 2931

Now multiplying the highest exponent prime factors to calculate the LCM of 12302 and 12306.

LCM(12302,12306) = 21 × 61511 × 31 × 71 × 2931
LCM(12302,12306) = 75694206