Find all three-digit numbers that are 12 times the sum of their digits.

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According to the condition, the number is divisible by 3. Therefore, the sum of its digits is also divisible by 3, which means the number itself is divisible by 9. In addition, it is divisible by 4. Therefore, we need to look for numbers that are divisible by 36. The sum of the digits of a three-digit number does not exceed 27, but the number 999 is not divisible by 12. Therefore, the sum of the digits of our number is no more than 18, and the number itself is no more than $18 \cdot 12=216$. It remains to check the numbers $108,144,180,216$.

## Answer

108.