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What is the Least Common Multiple of 12305 and 12315?

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 12305 and 12315 is 30307215.

LCM(12305,12315) = 30307215

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Least Common Multiple of 12305 and 12315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12305 and 12315, than apply into the LCM equation.

GCF(12305,12315) = 5
LCM(12305,12315) = ( 12305 × 12315) / 5
LCM(12305,12315) = 151536075 / 5
LCM(12305,12315) = 30307215

Least Common Multiple (LCM) of 12305 and 12315 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12305 and 12315. First we will calculate the prime factors of 12305 and 12315.

Prime Factorization of 12305

Prime factors of 12305 are 5, 23, 107. Prime factorization of 12305 in exponential form is:

12305 = 51 × 231 × 1071

Prime Factorization of 12315

Prime factors of 12315 are 3, 5, 821. Prime factorization of 12315 in exponential form is:

12315 = 31 × 51 × 8211

Now multiplying the highest exponent prime factors to calculate the LCM of 12305 and 12315.

LCM(12305,12315) = 51 × 231 × 1071 × 31 × 8211
LCM(12305,12315) = 30307215