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Home » The sum of the series is 6. - Coaching Toolbox

The sum of the series is 6. - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Wait — correction: in earlier computation, we had $4 \cdot 3 \cdot 5 \cdot 7 \cdot 17 \cdot 119$, but $119 = 7 \cdot 17$, and $119$ has repeated factor 7, so $7^1$ is sufficient.

📌 But $1,2,3,5,7,13,109$: all distinct primes → LCM = product of all distinct prime factors = $2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \cdot 109$

📌 $2730 \cdot 109 = 2730 \cdot 100 = 273000$, $2730 \cdot 9 = 24570$, total = $297,570$

📌 Can we do better? Try including $17$? Suppose $1, 2, 3, 5, 17, 19, 92$: sum = $1+2+3+5+17+19+92 = 140$

📌 LCM includes $2^2$, $3$, $5$, $17$, $19$, $92 = 4 \cdot 23$, so $23$ introduced.

📌 LCM = $ \text{LCM}(4,3,5,17,19,23) = 4 \cdot 3 \cdot 5 \cdot 17 \cdot 19 \cdot 23 $

📌 $4 \cdot 3 = 12$

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