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What is the Least Common Multiple of 12209 and 12223?

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 12223 is 149230607.

LCM(12209,12223) = 149230607

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Least Common Multiple of 12209 and 12223 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 12223, than apply into the LCM equation.

GCF(12209,12223) = 1
LCM(12209,12223) = ( 12209 × 12223) / 1
LCM(12209,12223) = 149230607 / 1
LCM(12209,12223) = 149230607

Least Common Multiple (LCM) of 12209 and 12223 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12209 and 12223. First we will calculate the prime factors of 12209 and 12223.

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 12223

Prime factors of 12223 are 17, 719. Prime factorization of 12223 in exponential form is:

12223 = 171 × 7191

Now multiplying the highest exponent prime factors to calculate the LCM of 12209 and 12223.

LCM(12209,12223) = 291 × 4211 × 171 × 7191
LCM(12209,12223) = 149230607