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Integer

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Manager
Joined: 25 Mar 2009
Posts: 52

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07 Apr 2009, 05:21
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Positive integer N divided by 3 remains 2; divided by 5 remains 4; divided by 7 remains 6. What is the smallest value of N?

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Manager
Joined: 02 Mar 2009
Posts: 123

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07 Apr 2009, 08:44
Since N is not divisible by the 3 prime factors, it will not be divisble by the LCM of these factors, ie 105. Since it leaves a remainder of '1 less than the prime number' to which it is divided, 1 less than 105, ie, 104 will meet the criteria for all the 3 numbers.

It makes intuitive sense to me. If someone has a better logic, kindly explain.
Director
Joined: 29 Aug 2005
Posts: 819

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07 Apr 2009, 12:14
Agree with the above logic.
Intern
Joined: 07 Feb 2009
Posts: 46

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09 Apr 2009, 03:32
Very well explained shkusira.

The only way these kind of questions can be solved is LCM/HCF.

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Re: Integer   [#permalink] 09 Apr 2009, 03:32
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