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What is the Least Common Multiple of 12214 and 12229?

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 12214 and 12229 is 149365006.

LCM(12214,12229) = 149365006

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Least Common Multiple of 12214 and 12229 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12214 and 12229, than apply into the LCM equation.

GCF(12214,12229) = 1
LCM(12214,12229) = ( 12214 × 12229) / 1
LCM(12214,12229) = 149365006 / 1
LCM(12214,12229) = 149365006

Least Common Multiple (LCM) of 12214 and 12229 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12214 and 12229. First we will calculate the prime factors of 12214 and 12229.

Prime Factorization of 12214

Prime factors of 12214 are 2, 31, 197. Prime factorization of 12214 in exponential form is:

12214 = 21 × 311 × 1971

Prime Factorization of 12229

Prime factors of 12229 are 7, 1747. Prime factorization of 12229 in exponential form is:

12229 = 71 × 17471

Now multiplying the highest exponent prime factors to calculate the LCM of 12214 and 12229.

LCM(12214,12229) = 21 × 311 × 1971 × 71 × 17471
LCM(12214,12229) = 149365006