Problem 52

Permuted multiples

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.

可以看出，$125874$和它的两倍$251748$拥有同样的数字，只是排列顺序不同。

有些正整数$x$满足$2x$、$3x$、$4x$、$5x$和$6x$都拥有与$x$相同的数字，求其中最小的正整数。