$1116 \div 36 = 31$, so divisible by 36
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- 252m + 108 \geq 1000 \Rightarrow 252m \geq 892 \Rightarrow m \geq \left\lceil \frac{892}{252} \right\rceil = 4
- For $m = 4$:
- n = 252 \cdot 4 + 108 = 1008 + 108 = 1116
- $1116 \div 7 = 159$ remainder $3$, so satisfies the second condition
- Thus, the smallest such number is $\boxed{1116}$.
- Question: A weather model uses a sequence of temperature readings: $12345, 12347, 12349, 12351$. What is the remainder when the sum of these readings is divided by 13?
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