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Home » From Rise to Ruin: The Complete Story of the Old Republic You Never Knew - Appcentric

From Rise to Ruin: The Complete Story of the Old Republic You Never Knew - Appcentric

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Question: A scientific simulation uses a time step increment that is the least common multiple of 18, 24, and 36. What is the greatest common divisor of this LCM and the number 432?

📌 Solution: First, compute $\mathrm{lcm}(18, 24, 36)$.

📌 $18 = 2 \cdot 3^2$

📌 Take max exponents: $2^3 \cdot 3^2 = 8 \cdot 9 = 72$. So $\mathrm{lcm} = 72$.

📌 Now compute $\gcd(72, 432)$.

📌 Since $72 \mid 432$ (because $432 \div 72 = 6$), the GCD is $72$.

📌 Alternatively, $432 = 6 \cdot 72$, so $\gcd = 72$.

📌 Thus, the answer is $\boxed{72}$.Question: A renewable energy startup is designing a rectangular solar panel array with a fixed perimeter of 80 meters. What is the maximum possible area of the array?

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