# Multiplication Or Rearrangement

**Number Theory**Level 5

What is the smallest number that, when multiplied by 4, is simply the original number with the rightmost digit moved to the front of the number?

As an explicit example, if we replace the number 4 with 5 above, then we have \(5\times142857=714285\).

(Note that here I multiplied by 5, while the question asks for a number that works when multiplied by 4.)

**Note:** Don't consider numbers with leading zeroes.