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What is the Least Common Multiple of 12705 and 12715?

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 12705 and 12715 is 32308815.

LCM(12705,12715) = 32308815

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Least Common Multiple of 12705 and 12715 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12705 and 12715, than apply into the LCM equation.

GCF(12705,12715) = 5
LCM(12705,12715) = ( 12705 × 12715) / 5
LCM(12705,12715) = 161544075 / 5
LCM(12705,12715) = 32308815

Least Common Multiple (LCM) of 12705 and 12715 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12705 and 12715. First we will calculate the prime factors of 12705 and 12715.

Prime Factorization of 12705

Prime factors of 12705 are 3, 5, 7, 11. Prime factorization of 12705 in exponential form is:

12705 = 31 × 51 × 71 × 112

Prime Factorization of 12715

Prime factors of 12715 are 5, 2543. Prime factorization of 12715 in exponential form is:

12715 = 51 × 25431

Now multiplying the highest exponent prime factors to calculate the LCM of 12705 and 12715.

LCM(12705,12715) = 31 × 51 × 71 × 112 × 25431
LCM(12705,12715) = 32308815