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What is the Least Common Multiple of 12357 and 12372?

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 12357 and 12372 is 50960268.

LCM(12357,12372) = 50960268

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Least Common Multiple of 12357 and 12372 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12357 and 12372, than apply into the LCM equation.

GCF(12357,12372) = 3
LCM(12357,12372) = ( 12357 × 12372) / 3
LCM(12357,12372) = 152880804 / 3
LCM(12357,12372) = 50960268

Least Common Multiple (LCM) of 12357 and 12372 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12357 and 12372. First we will calculate the prime factors of 12357 and 12372.

Prime Factorization of 12357

Prime factors of 12357 are 3, 1373. Prime factorization of 12357 in exponential form is:

12357 = 32 × 13731

Prime Factorization of 12372

Prime factors of 12372 are 2, 3, 1031. Prime factorization of 12372 in exponential form is:

12372 = 22 × 31 × 10311

Now multiplying the highest exponent prime factors to calculate the LCM of 12357 and 12372.

LCM(12357,12372) = 32 × 13731 × 22 × 10311
LCM(12357,12372) = 50960268