Remark
Fun question. It has to have at least three 1s in it. that's because it has to be divisible by 3 and 5. So to get it divisible by 3 you need to have something that will add up to 3 or 3n where n is any number above 0.
The 5 part comes into it by adding a zero on the end. Something divisible by 5 must and in 0 or 5. Since 5 is not permitted, the number has to end in zero.
Answer. The Smallest number must be 1110