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Home » Set the exponents equal: \(3x = 6\). - Treasure Valley Movers

Set the exponents equal: \(3x = 6\). - Treasure Valley Movers

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 Solution: We seek the smallest multiple of $\mathrm{lcm}(1,2,\dots,12)$ greater than 1,000,000.

📌 Factor each number from 1 to 12:

📌 $2^3$ (from 8),

📌 $3^2$ (from 9),

📌 Others: 4 = $2^2$, 6 = $2\cdot3$, 10 = $2\cdot5$, 12 = $2^2\cdot3$. So highest powers:

📌 \mathrm{lcm} = 2^3 \cdot 3^2 \cdot 5 \cdot 7 \cdot 11 = 8 \cdot 9 \cdot 5 \cdot 7 \cdot 11.

📌 $8 \cdot 9 = 72$,

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