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Find the smallest positive integer n so that 14n, 16n, 18n, and 20n all have the same number of divisors.

 May 2, 2020
 #1
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Hint: Find the factors then find the LCM.

 #2
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This is the lcm of (14, 16, 18, 20)  .

 

The prime factorization will be 7 x 2^8 x 3^2 x 5. We can strip a lot of factors from this.

 

This is just 7 x 16 x 9 x 5 which is 7! or 5040

 May 3, 2020

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