BMAD Posted October 31, 2014 Report Share Posted October 31, 2014 What is the smallest number that is divisible by 2, 3, 4, 5 and 6 with one digit left over, yet is evenly divided by 7? The answer is pretty straightforward but I am interested in seeing if there are various proofs to this problem. Quote Link to comment Share on other sites More sharing options...
0 karthickgururaj Posted October 31, 2014 Report Share Posted October 31, 2014 It is indeed straightforward, so let me start with.. Take the LCM of 2, 3, 4, 5 and 6 = 4 x 3 x 5 = 60. We want to find a multiple of 60 that will give "-1 mod 7" or equivalently, "6 mod 7". It is easy to see that, 60 = 4 mod 7. 60 x 5 = (4x5) mod 7 = 6 mod 7. So, (60 x 5) + 1 = 301 is the number we are looking for. Quote Link to comment Share on other sites More sharing options...
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BMAD
What is the smallest number that is divisible by 2, 3, 4, 5 and 6 with one digit left over, yet is evenly divided by 7?
The answer is pretty straightforward but I am interested in seeing if there are various proofs to this problem.
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