The question is ambiguous. It could refer to the smallest number divisible by both 9 and 11 (the least common multiple), or the smallest number formed using the digits 9 and 11 (if interpreted as single digits). Let's address both possibilities:
Interpretation 1: Least Common Multiple (LCM)
The smallest number divisible by both 9 and 11 is their Least Common Multiple (LCM). Since 9 and 11 are relatively prime (they share no common factors other than 1), their LCM is simply their product.
LCM(9, 11) = 9 * 11 = 99
Therefore, the smallest number divisible by both 9 and 11 is 99.
Interpretation 2: Smallest Number Formed by Digits 9 and 11
If we interpret "number of 9 and 11" as referring to the digits available, then the smallest number we can form is 9. While 11 is smaller than 9 numerically, the question seems to imply using both "9" and "11." However, since the question asks for a single "smallest number", the most reasonable and numerically sound answer would be 9.
In the very literal sense, you cannot create a standard number with the digits 9 and 11, since 11 is not a single digit.
Conclusion:
Given the ambiguity, the most probable interpretation is the Least Common Multiple. Therefore, the smallest number is 99.
