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Home » Therefore, there are \(\boxed60\) ways to choose and arrange 3 minerals from 5. - Carbonext

Therefore, there are \(\boxed60\) ways to choose and arrange 3 minerals from 5. - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Question:** An archaeologist uncovers two ancient pottery fragments with volumes measured at 12 liters and 27 liters. Find the least common multiple (LCM) of the volumes in liters.

📌 To find the least common multiple of 12 and 27, first determine their prime factorizations:

📌 \(12 = 2^2 \times 3\)

📌 \(27 = 3^3\)

📌 For \(2\), the highest power is \(2^2\)

📌 For \(3\), the highest power is \(3^3\)

📌 LCM = 2^2 \times 3^3 = 4 \times 27 = 108

📌 Therefore, the least common multiple of the volumes is \(\boxed{108}\) liters.

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