jmc

We divide 1000 by 47 and get a remainder of 13. Therefore, if we subtract 13 from 1000, we should get an integer divisible by 47. Since $1000-13=987$ and 987 is divisible by 47, we can then add 47 to 987 to get the smallest four-digit integer that is divisible by 47, namely $987+47=\boxed{1034}$.