What 6 digit number, with 6 different digits, when multiplied by all integers

up to 6, circulates its digits through all 6 possible positions, as follows
ABCDEF * 1 = ABCDEF ABCDEF * 3 = BCDEFA ABCDEF * 2 = CDEFAB ABCDEF * 6 = DEFABC ABCDEF * 4 = EFABCD ABCDEF * 5 = FABCDE

Circular Solution

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