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What is the Least Common Multiple of 12193 and 12209?

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 12193 and 12209 is 148864337.

LCM(12193,12209) = 148864337

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Least Common Multiple of 12193 and 12209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12193 and 12209, than apply into the LCM equation.

GCF(12193,12209) = 1
LCM(12193,12209) = ( 12193 × 12209) / 1
LCM(12193,12209) = 148864337 / 1
LCM(12193,12209) = 148864337

Least Common Multiple (LCM) of 12193 and 12209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12193 and 12209. First we will calculate the prime factors of 12193 and 12209.

Prime Factorization of 12193

Prime factors of 12193 are 89, 137. Prime factorization of 12193 in exponential form is:

12193 = 891 × 1371

Prime Factorization of 12209

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

12209 = 291 × 4211

Now multiplying the highest exponent prime factors to calculate the LCM of 12193 and 12209.

LCM(12193,12209) = 891 × 1371 × 291 × 4211
LCM(12193,12209) = 148864337