Here’s a variation on a golden oldie. It was a very similar problem that got me hooked on ToM and caused me to learn about modulo arithmetic. Hey, it’s this or nothing.
What is the smallest positive integer that ends with a 6, becomes 6 times as large when the 6 is moved to the start.
e.g. I want something along the lines of: 6123 = 6*1236.
You’ll find that the Windows calculator could be useful for this problem.
You’ll find http://www.wolframalpha.com useful for the calculations.