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tlc songs no scrubs lyrics - Leaselab

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 $30 = 2 \cdot 3 \cdot 5$.

📌 The LCM is obtained by taking the highest power of each prime:

📌 $\mathrm{LCM}(18, 30) = 2 \cdot 3^2 \cdot 5 = 90$.

📌 Thus, the two markers will next peak together in \(\boxed{90}\) days.

📌 Question: A paleobotanist is examining fossilized leaf arrangements where the number of veins in two different species are represented by positive integers \(a\) and \(b\) such that \(a + b = 2024\) and \(\gcd(a, b)\) is maximized. What is the maximum possible value of \(\gcd(a, b)\)?

📌 Solution: Let \(d = \gcd(a, b)\), so \(a = d \cdot m\), \(b = d \cdot n\), with \(m\) and \(n\) coprime positive integers. Then:

📌 a + b = d(m + n) = 2024

📌 Thus, \(d\) must be a divisor of 2024, and \(m + n = \frac{2024}{d}\). To maximize \(d\), we minimize \(m + n\), which is minimized when \(m + n = 2\), since \(m, n \geq 1\) and coprime. The only such pair is \(m = 1\), \(n = 1\), which are coprime. Then:

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