The question is:
Determine the smallest multiple of 9 which divided by each of the numbers 2, 5 and 11 leaves a remainder 1.
The answer is 441.
What I did when I tried solving this was to set up 3 different equations:
- 9n = 1 mod 2
- 9n = 1 mod 5
- 9n = 1 mod 11
And solved for each n. I got values of 27, 54 and 108 respectively. I didn't really know where to go from here to get the answer of 441. I think I may be on the wrong path, I'm not really sure. If someone can enlighten me as to why the answer is 441, it will be greatly appreciated.