7. 【Solution】From the statement "the sum of the digits of the addend is three times the sum of the digits of the sum," we can deduce two points: (1) The addend can be divisible by 3. (2) When performing the addition, the sum of the units digits must carry over, otherwise the sum of the digits of the result would only increase.

From the first point, we can conclude that the addend is among $12, 15, 18 \cdots \cdots$.
From the second point, we can conclude that the smallest addend is 18, at which point the sum of the digits $1+8=9$, which is exactly three times the sum of the digits of the sum 21, which is $2+1=3$.
Therefore, the smallest addend that satisfies the problem is 18.
7. In the addition problem on the right, the sum of the digits of the addend is three times the sum of the digits of the sum. What is the smallest possible addend?



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