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📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Thus, $ P $ is divisible by $ \text{lcm}(8, 3) = 24 $.

📌 We check if a larger fixed divisor is guaranteed:

📌 Not always divisible by 5 (e.g., $ n = 1 $: product = 24, not divisible by 5).

📌 Not always divisible by higher powers (e.g., $ n = 1 $: product = 24, not divisible by 48).

📌 Thus, the largest integer that must divide the product of any four consecutive integers is $ \boxed{24} $.

📌 Question: A mammalogist observes that a species of Arctic foxes returns to its den every 5 days, and another species every 7 days. If both species were seen at the den on day 1, on which day will they next be seen together?

📌 Solution: We are to find the least common multiple of 5 and 7:

📌 \text{lcm}(5, 7) = 35

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