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📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 First, compute the least common multiple (LCM) of $12$ and $18$.

📌 \text{lcm}(12, 18) = \text{lcm}(2^2 \cdot 3, 2 \cdot 3^2) = 2^2 \cdot 3^2 = 36

📌 The smallest prime greater than $10$ is $11$, so its square is $11^2 = 121$.

📌 We now seek the smallest four-digit number divisible by both $36$ and $121$.

📌 \text{lcm}(36, 121) = \text{lcm}(2^2 \cdot 3^2, 11^2) = 2^2 \cdot 3^2 \cdot 11^2 = 4 \cdot 9 \cdot 121 = 36 \cdot 121 = 4356

📌 Since $4356$ is a four-digit number and divisible by both $36$ and $121$, it is the smallest such number.

📌 \boxed{4356}

📌 Question: How many integers between $1$ and $200$, inclusive, are congruent to $3 \pmod

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