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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Thus, the maximum LCM occurs when the numbers are chosen to include as many distinct prime powers as possible, especially large primes.

📌 The configuration $1, 2, 3, 5, 7, 13, 109$ gives:

📌 \text{LCM}(1,2,3,5,7,13,109) = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 109

📌 $2 \cdot 3 = 6$

📌 $6 \cdot 5 = 30$

📌 $30 \cdot 7 = 210$

📌 $210 \cdot 13 = 2730$

📌 $2730 \cdot 109 = 2730 \cdot (100 + 9) = 273000 + 24570 = 297,570$

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