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