How to find the smallest number with just 0 and 1 which is divided by a given number?

Question

Every positive integer divide some number whose representation (base 10) contains only zeroes and ones.

One can prove that:

Consider the numbers 1, 11, 111,

Answer 1

Here is a C# solution using linked list

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Collections;

namespace ConsoleApplication1
{
    class Program
    {
        public static void print(LinkedList lst)
        {
            foreach(int i in lst)
            {
                Console.Write(i);
            }
        }

        static void Main(string[] args)
        {
            int number = Convert.ToInt32(Console.ReadLine());
            int product;
            LinkedList list = new LinkedList();
            bool Istrue = true;
            int range = 1;

            while (range <= 10) { 
                Istrue = true;
                product = number * range;
                while (product > 0)
                {
                    list.AddFirst(product % 10);
                    product /= 10;

                }

                foreach (int i in list)
                {
                    if (i > 1) Istrue = false;
                }

                if (Istrue) { print(list); break; }
                else
                {
                    list.Clear();   
                }

                range++;    
            }

            Console.WriteLine("Done");

            string s = Console.ReadLine();
        }
    }
}