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No New Digits

A six-digit number represented by ABCDEF (each letter represents a different number) can be multiplied by 2, 3, 4, 5, and 6 and yet no new digits appear in the result. As a matter of fact, all the digits are rotated. What is the number?

142857 (The first 6 digits of 1/7)

2 x 142857 = 285714
3 x 142857 = 428571
4 x 142857 = 571428
5 x 142857 = 714285
6 x 142857 = 857142


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