Find the smallest binary digit multiple of given number
No idea where you got that 9 from, in the last line of the question.

Having said that, You have to know that "concatenating" numbers is equivalent to multiplying the first number by a power of 10, followed by adding the second number. E.g. 42|7 = (42*10)+7.

Now obviously 42 is divisible by 6, but therefore so is 420. Furthermore, 42 mod 5 = 2, therefore 420 mod 5 = 20 mod 5. "42 is divisible by 6" in fact means "42 mod 6 = 0"