138 divided by 42 gives 3 with remainder 12.
63 divided by 17 also gives 3 with remainder 12.
So, we need to build another division that gives gives 3 with remainder 12.
If we want a remainder of 12, we must divide by at least 13 (the remainder can't be greater than what you're dividing for).
Since
[tex]13*3+12 = 39+12=51[/tex]
We have that 51 divided by 13 gives 3 with remainder 12.
In general, pick any number k>12 and define
[tex]n=3k+12[/tex]
And you will be sure that n divided by k gives 3 with remainder 12.
