A Number Theory Problem by Bob Kadylo

Find the smallest positive integer $x$ , such that $2x, 3x, 4x, 5x$ and $6x$ , contain the same digits.

In other words, $x$ , is the smallest natural number which has the amazing property that $1x, 2x, 3x, 4x, 5x$ and $6x$ , are ALL permutations of the same set of digits .

Note: I found this while working on a problem by Syed Baqir and thought it was worth sharing with the Brilliant community.