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Home » Secret Dates & Secrets Revealed: The Sonic Timeline You Never Knew! - AMAZONAWS

Secret Dates & Secrets Revealed: The Sonic Timeline You Never Knew! - AMAZONAWS

Secret Dates & Secrets Revealed: The Sonic Timeline You Never Knew

📅 March 11, 2026 👤 scraface

Mar 11, 2026

Secret Dates & Secrets Revealed: The Sonic Timeline You Never Knew!

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📌 Solution: Let \(d = \gcd(a, b)\). Then we can write \(a = d \cdot m\) and \(b = d \cdot n\), where \(m\) and \(n\) are coprime positive integers. The total road length is \(a + b = d(m + n) = 1000\). So \(d\) must divide 1000. To maximize \(d\), we minimize \(m + n\), subject to \(m\) and \(n\) being coprime positive integers. The smallest possible value of \(m + n\) is 2, which occurs when \(m = n = 1\), and they are coprime. This gives \(d = \frac{1000}{2} = 500\). Since \(m = 1\) and \(n = 1\) are coprime, this is valid. Therefore, the largest possible value of \(\gcd(a, b)\) is \(\boxed{500}\).

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