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What is the Least Common Multiple of 12192 and 12205?

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 12192 and 12205 is 148803360.

LCM(12192,12205) = 148803360

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Least Common Multiple of 12192 and 12205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12192 and 12205, than apply into the LCM equation.

GCF(12192,12205) = 1
LCM(12192,12205) = ( 12192 × 12205) / 1
LCM(12192,12205) = 148803360 / 1
LCM(12192,12205) = 148803360

Least Common Multiple (LCM) of 12192 and 12205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12192 and 12205. First we will calculate the prime factors of 12192 and 12205.

Prime Factorization of 12192

Prime factors of 12192 are 2, 3, 127. Prime factorization of 12192 in exponential form is:

12192 = 25 × 31 × 1271

Prime Factorization of 12205

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

12205 = 51 × 24411

Now multiplying the highest exponent prime factors to calculate the LCM of 12192 and 12205.

LCM(12192,12205) = 25 × 31 × 1271 × 51 × 24411
LCM(12192,12205) = 148803360