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Home » The final answer is \(\boxed120\). - Leaselab

The final answer is \(\boxed120\). - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question: A spaceship’s navigation system uses a 13-bit code and a 17-bit engine control sequence. What is the smallest number of distinct sequences required to uniquely align both systems simultaneously?

📌 Solution: The smallest number of distinct sequences is the least common multiple (LCM) of 13 and 17.

📌 Since 13 and 17 are primes, $\text{LCM}(13, 17) = 13 \times 17 = 221$.

📌 Thus, the answer is $\boxed{221}$.

📌 Question: A palynologist observes pollen count patterns that repeat every 2025 days and spore distribution cycles every 1515 days. What is the least number of days after which both patterns align?

📌 Solution: The alignment occurs at the least common multiple of 2025 and 1515.

📌 Compute $\text{LCM}(2025, 1515) = \frac{2025 \times 1515}{\gcd(2025, 1515)}$.

📌 From prior calculation, $\gcd(2025, 1515) = 15$.

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