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What is the Least Common Multiple of 17415 and 17430?

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 17415 and 17430 is 20236230.

LCM(17415,17430) = 20236230

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Least Common Multiple of 17415 and 17430 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17415 and 17430, than apply into the LCM equation.

GCF(17415,17430) = 15
LCM(17415,17430) = ( 17415 × 17430) / 15
LCM(17415,17430) = 303543450 / 15
LCM(17415,17430) = 20236230

Least Common Multiple (LCM) of 17415 and 17430 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17415 and 17430. First we will calculate the prime factors of 17415 and 17430.

Prime Factorization of 17415

Prime factors of 17415 are 3, 5, 43. Prime factorization of 17415 in exponential form is:

17415 = 34 × 51 × 431

Prime Factorization of 17430

Prime factors of 17430 are 2, 3, 5, 7, 83. Prime factorization of 17430 in exponential form is:

17430 = 21 × 31 × 51 × 71 × 831

Now multiplying the highest exponent prime factors to calculate the LCM of 17415 and 17430.

LCM(17415,17430) = 34 × 51 × 431 × 21 × 71 × 831
LCM(17415,17430) = 20236230