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What is the Least Common Multiple of 12259 and 12272?

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 12259 and 12272 is 11572496.

LCM(12259,12272) = 11572496

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Least Common Multiple of 12259 and 12272 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12259 and 12272, than apply into the LCM equation.

GCF(12259,12272) = 13
LCM(12259,12272) = ( 12259 × 12272) / 13
LCM(12259,12272) = 150442448 / 13
LCM(12259,12272) = 11572496

Least Common Multiple (LCM) of 12259 and 12272 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12259 and 12272. First we will calculate the prime factors of 12259 and 12272.

Prime Factorization of 12259

Prime factors of 12259 are 13, 23, 41. Prime factorization of 12259 in exponential form is:

12259 = 131 × 231 × 411

Prime Factorization of 12272

Prime factors of 12272 are 2, 13, 59. Prime factorization of 12272 in exponential form is:

12272 = 24 × 131 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 12259 and 12272.

LCM(12259,12272) = 131 × 231 × 411 × 24 × 591
LCM(12259,12272) = 11572496