Problem 51950. Find the smallest integer m such that n divides m!

Created by ChrisR

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Write a function that takes an integer n and finds the smallest integer m whose factorial is divisible by n. For example, if , then the smallest factorial that is a multiple of n is 5! = 120; therefore, . 

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Last Solution submitted on Nov 29, 2025

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David Hill on 3 Jun 2021

Chris, please check test 21. The factors of 1535238 include two 67's, therefore it seems to me the solution should be 134.

Are Mjaavatten on 3 Jun 2021

David: Take another look. ChrisR's anti-lookup trick lets correct solutions pass the test!

ChrisR on 3 Jun 2021

David, you are correct for Kempner(1535238), but that test asks for Kempner(Kempner(Kempner(1535238))).

Rafael S.T. Vieira on 25 Nov 2022

Unfortunately, it does not stop lookup tables since 134 factors to 2 and 67, which means it obtains the same result as a lookup table. Kempner(Kempner(Kempner(1535238))) will do 134 -> 67 -> 67 and a lookup table 67->67->67.

Rafael S.T. Vieira on 25 Nov 2022

May I suggest using Kempner(Kempner(Kempner(123456787654321))+10) as a test against lookup tables?

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