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What is the Least Common Multiple of 12209 and 12214?

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 12209 and 12214 is 149120726.

LCM(12209,12214) = 149120726

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Least Common Multiple of 12209 and 12214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12209 and 12214, than apply into the LCM equation.

GCF(12209,12214) = 1
LCM(12209,12214) = ( 12209 × 12214) / 1
LCM(12209,12214) = 149120726 / 1
LCM(12209,12214) = 149120726

Least Common Multiple (LCM) of 12209 and 12214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12209 and 12214. First we will calculate the prime factors of 12209 and 12214.

Prime Factorization of 12209

Prime factors of 12209 are 29, 421. Prime factorization of 12209 in exponential form is:

12209 = 291 × 4211

Prime Factorization of 12214

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

12214 = 21 × 311 × 1971

Now multiplying the highest exponent prime factors to calculate the LCM of 12209 and 12214.

LCM(12209,12214) = 291 × 4211 × 21 × 311 × 1971
LCM(12209,12214) = 149120726