2017/036) Find the smallest multiple of 15 such that each digit of the multiple is either 0 or 8

Because it is multiple of 15 and 15 = 3 * 5 so it is multiple of 3 and 5. So the unit digit is zero. As 8 is not multiple of 3 there should be 3 8's for the number to be multiple of 3  and the digit cannot be the unit position. Hence the smallest number is 8880.