If we choose 12 x 89 = 1068, it is not divisible by 11.

We can continue this process until we find a number that satisfies the conditions.

Let’s try:

12 x 92 = 1104.

This number works because it is divisible by both 11 and 12.

Therefore, a five-digit number that is divisible by 11 and 12 is 1104.