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Home » The LCM takes the highest powers of all primes: - Dachbleche24

The LCM takes the highest powers of all primes: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A mammalogist records that a caribou herd migrates 18 km per day during peak migration. If they cover 324 km over several days but rest every fifth day (migrating only on non-rest days), how many total days does the migration take?

📌 Daily migration = 18 km

📌 Total distance = 324 km

📌 Without rest days, number of active days = 324 ÷ 18 = 18

📌 Rest days occur every 5th day (i.e., after every 4 active days), so rest days = floor(18 / 4) = 4 (on days 5,10,15,20)

📌 But last rest day is before completing 18 days — check: days 1–4 active, day 5 rest → cycle of 5 days gives 4 km

📌 4 km per 5-day cycle → 324 ÷ 4 = 81 cycles → 81 × 5 = 405 days

📌 But 18 days active is more than needed → refine:

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