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What is the Least Common Multiple of 12204 and 12213?

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 12204 and 12213 is 16560828.

LCM(12204,12213) = 16560828

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Least Common Multiple of 12204 and 12213 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12204 and 12213, than apply into the LCM equation.

GCF(12204,12213) = 9
LCM(12204,12213) = ( 12204 × 12213) / 9
LCM(12204,12213) = 149047452 / 9
LCM(12204,12213) = 16560828

Least Common Multiple (LCM) of 12204 and 12213 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12204 and 12213. First we will calculate the prime factors of 12204 and 12213.

Prime Factorization of 12204

Prime factors of 12204 are 2, 3, 113. Prime factorization of 12204 in exponential form is:

12204 = 22 × 33 × 1131

Prime Factorization of 12213

Prime factors of 12213 are 3, 23, 59. Prime factorization of 12213 in exponential form is:

12213 = 32 × 231 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 12204 and 12213.

LCM(12204,12213) = 22 × 33 × 1131 × 231 × 591
LCM(12204,12213) = 16560828