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Permuted multiples

Problem 52 Published on Friday, 12th September 2003, 06:00 pm; Solved by 56303;
Difficulty rating: 5%

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.