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smallest possible multiple of a no by 1 digit only

Source: 7th Gulf Math Olympiad 2019 GMO p2

December 31, 2019
number theoryDigitsmultiple

Problem Statement

1. Find NN, the smallest positive multiple of 4545 such that all of its digits are either 77 or 00. 2. Find MM, the smallest positive multiple of 3232 such that all of its digits are either 66 or 11. 3. How many elements of the set {1,2,3,...,1441}\{1,2,3,...,1441\} have a positive multiple such that all of its digits are either 55 or 22?
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