Is it a Cyclic number? A cyclic number is a number of "n" digits that when multiplied by 1, 2, 3,...n, results in the same digits but in a different order. 

For example, the number 142,857 is a cyclic number since 142,857 x 2 = 285,714, 142,857 x 3 = 428,571, 142,857 x 4 = 571,428, and so on. Given an integer input, determine if it is a cyclic number by outputting a truthy value if it is, and a falsy value if not.

Also, to be clear, the input can contain leading 0's: e.g. 0344827586206896551724137931

This is because, if leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal.

Since it is code-golf, shortest answer in bytes wins!
Actually, 18 bytes

;;ru@≈*♂$♂S♂≈╔@S≈=


Try it online! (expects quoted input)

Explanation:

;;ru@≈*♂$♂S♂≈╔@S≈=
;;                  duplicate input twice
  ru                range(1, len(input)+1)
    @≈              convert input to an integer
      *             multiply input by each element in range
       ♂$♂S♂≈       convert each product to a string, sort the digits, and convert back to int
             ╔      uniquify: remove duplicate elements
              @S≈   sort input and convert to int
                 =  compare equality