If you multiple 37 by 3y you will get a three-digit number that is all y's. For example, 37 x (3 x 1) = 111 and 37 x (3 x 7) = 777.
The same applies with 15,873 and 7y, and 8,547 and 13y.
These are known as Magic Numbers.
The puzzle is to find the smallest Magic Number for 17. That is the smallest number that when multiplied by 17y produces a number in which every digit is y.
To find this number try to divide 17 into 111, 1,111, 11,111 and so on until you find one with no remainder. That is, the smallest number of the pattern 111 . . . 111 that is a multiple of 17.
The number is 1,111,111,111,111,111 and the number is 65,359,477,124,183. That is, 65,359,477,124,183 x 17 = 1,111,111,111,111,111.
So the answer is 65,359,477,124,183