What is the smallest number so that if you move its last digit to the beginning (for example, turning 1234 into 4123) you get a new number that is an integer multiple of the original number?
The stating of the problem does not say that the beginning numbers must be integers.
therefore,
0.0.....1 will always become 10
therefore, the number could be infinitely small.
If we say that the first number must be an integer (including the rule that the number formed must be new), 10 is the smallest solution:
10 becomes 01 (1*10)
Therefore, the solution 102564 is the smallest only if the the number does not end in '0' and must begin as a natural number.
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