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What is the Least Common Multiple of 12205 and 12210?

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 12205 and 12210 is 29804610.

LCM(12205,12210) = 29804610

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Least Common Multiple of 12205 and 12210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12205 and 12210, than apply into the LCM equation.

GCF(12205,12210) = 5
LCM(12205,12210) = ( 12205 × 12210) / 5
LCM(12205,12210) = 149023050 / 5
LCM(12205,12210) = 29804610

Least Common Multiple (LCM) of 12205 and 12210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12205 and 12210. First we will calculate the prime factors of 12205 and 12210.

Prime Factorization of 12205

Prime factors of 12205 are 5, 2441. Prime factorization of 12205 in exponential form is:

12205 = 51 × 24411

Prime Factorization of 12210

Prime factors of 12210 are 2, 3, 5, 11, 37. Prime factorization of 12210 in exponential form is:

12210 = 21 × 31 × 51 × 111 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 12205 and 12210.

LCM(12205,12210) = 51 × 24411 × 21 × 31 × 111 × 371
LCM(12205,12210) = 29804610