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What is the Least Common Multiple of 17405 and 17414?

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 17405 and 17414 is 303090670.

LCM(17405,17414) = 303090670

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Least Common Multiple of 17405 and 17414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17405 and 17414, than apply into the LCM equation.

GCF(17405,17414) = 1
LCM(17405,17414) = ( 17405 × 17414) / 1
LCM(17405,17414) = 303090670 / 1
LCM(17405,17414) = 303090670

Least Common Multiple (LCM) of 17405 and 17414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17405 and 17414. First we will calculate the prime factors of 17405 and 17414.

Prime Factorization of 17405

Prime factors of 17405 are 5, 59. Prime factorization of 17405 in exponential form is:

17405 = 51 × 592

Prime Factorization of 17414

Prime factors of 17414 are 2, 8707. Prime factorization of 17414 in exponential form is:

17414 = 21 × 87071

Now multiplying the highest exponent prime factors to calculate the LCM of 17405 and 17414.

LCM(17405,17414) = 51 × 592 × 21 × 87071
LCM(17405,17414) = 303090670