Find the smallest 4-digit number which leaves a remainder of 9 when divided by 33, 44 and 66.

LCM(33, 44, 66) = $2^2\times 3\times 11=132$, so the number has the form $132k+9$. For $k=7$ this gives 933, which has only 3 digits; for $k=8$ it gives 1065, the smallest 4-digit value. Answering 1056 gives the multiple of the LCM without the remainder, and 1047 subtracts the remainder instead of adding it.