Find the smallest positive integer that leaves a remainder of 5 when divided by 7, a remainder of 6 when divided by 11, and a remainder of 4 when divided by 13.

Answer 1

leaving remainder of 5 when divided by 7 ...
must be multiples of 7 plus 5 :
12 19 26 33 40 47 54 61 68 75 82 89 96 103 110 ..
remainder of 6 when divided by 11
17 28 39 50 61 72 83 94 105 116 127 ...
remainder of 4 when divided by 13
17 30 43 56 69 82 95 108 121 ...
noting so far, I will let you go on for a bit more.

Looking for a common number in all 3 lists,