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When the positive integer x is divided by each of 4, 5, 6, and 7, it has a remainder of 3. What is the sum of the three smallest possible values of x?

 Feb 1, 2021
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Using CRT + MMI

 

x mod 4 = 3
x mod 5 = 3
x mod 6 = 3
x mod 7 = 3, solve  for x

 

LCM[4, 5, 6, 7]==420

 

x =420n  + 3, where n =0, 1, 2, 3.......etc.

 

The smallest value of x is when n = 0, which means x = 3

So, the sum of 3 smallest values of x are:

3  +  423  +  843 ==1,269

 Feb 1, 2021

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