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Home » Discover the Mind-Blowing Gold Experience Requiem No One Told You About - Silent Sales Machine

Discover the Mind-Blowing Gold Experience Requiem No One Told You About - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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?

📌 Solution: The perimeter of a rectangle is given by $ P = 2(l + w) $, where $ l $ is length and $ w $ is width. Given $ 2(l + w) = 80 $, we simplify to $ l + w = 40 $. The area $ A = lw $. Express $ w = 40 - l $, so $ A = l(40 - l) = 40l - l^2 $. This quadratic equation opens downward, and its maximum occurs at the vertex $ l = \frac{-b}{2a} = \frac{-40}{-2} = 20 $. Substituting $ l = 20 $, $ w = 20 $, so $ A = 20 \times 20 = 400 $. The maximum area is $\boxed{400}$.

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