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Home » Calculate the concentration after 3 hours: - ToelettAPP

Calculate the concentration after 3 hours: - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 dk + dl = 150 \implies d(k + l) = 150

📌 To maximize \( d \), minimize \( k + l \). Since \(\gcd(k, l) = 1\), the smallest sum is 2 (when \( k = 1 \), \( l = 1 \)). Then:

📌 d imes 2 = 150 \implies d = 75

📌 Since 75 divides 150 and \( k + l = 2 \) satisfies coprimality, the largest possible \(\gcd(p, q)\) is \(oxed{75}\).

📌 An entomologist is examining the cycles of a rare insect species, where the cycle length is represented by a three-digit integer \( z \) such that \( z \) is divisible by 7, 11, and 13. What is the smallest such \( z \)?

📌 Since \( z \) is divisible by 7, 11, and 13, compute the least common multiple:

📌 ext{lcm}(7, 11, 13) = 7 imes 11 imes 13 = 1001

📌 But 1001 is a four-digit number. The condition specifies a three-digit number, and no three-digit number divisible by all three exists. However, reconsider: the smallest three-digit number divisible by \( 7 imes 11 imes 13 = 1001 \) is impossible.

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