2018 Solution 04

This time we take a break from circuit design. Every positive integer has a product that, when expressed in base ten (like normal human readable numbers), is comprised entirely of zeros and ones. Write a program to find the least multiplier m for a given number n, that results in a product p of the required form. The product n*0=0 does not count as an answer.
Multiplicand, n Multiplier, m Product, p​​2 5 10​​3 37 111​​4 25 100​​9 1122334455667789 111 111 111 111 111 111​​​​​​