It can be seen that the number, \(125874\), and its double, \(251748\), contain exactly the same digits, but in a different order.
Find the smallest positive integer, \(x\), such that \(2x\), \(3x\), \(4x\), \(5x\), and \(6x\), contain the same digits.
No code required for this one! Consider the decimal expansions of the following fractions:
\begin{align} 1/7 &= 0.142857 \, 142857 \, 142857\ldots \\ 2/7 &= 0.285714 \, 285714 \, 285714\ldots \\ 3/7 &= 0.428571 \, 428571 \, 428571\ldots \\ 4/7 &= 0.571428 \, 571428 \, 571428\ldots \\ 5/7 &= 0.714285 \, 714285 \, 714285\ldots \\ 6/7 &= 0.857142 \, 857142 \, 857142\ldots \end{align}Cyclic numbers are the repeating parts of unit fractions, and \(142857\) is well known as the smallest nontrivial cyclic number, as well as the only one with no leading zeros.