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📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 A pharmacologist is analyzing the molecular structure of a new compound. They need to determine the remainder when the sum of the cubes of the first 10 natural numbers is divided by 11. What is this remainder?

📌 An engineer is designing a new sustainable drainage system in Singapore. They need to find the smallest four-digit number that is divisible by both 7 and 13. What is this number?

📌 To find the smallest four-digit number divisible by both 7 and 13, we first find their least common multiple (LCM).

📌 Since 7 and 13 are coprime, their LCM is:

📌 Now, we find the smallest four-digit number divisible by 91. The smallest four-digit number is 1000. We calculate:

📌 Thus, the smallest four-digit number divisible by 91 is:

📌 Thus, there are 18 such integer solutions.

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