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Home » The probability is $\boxed{\dfrac827}$. - Aurero

The probability is $\boxed{\dfrac827}$. - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Here, \( a = 10 \), \( b = 15 \), so:

📌 \gcd(10, 15) = 5

📌 \gcd(2^{10} - 1, 2^{15} - 1) = 2^5 - 1 = 32 - 1 = 31

📌 The greatest common divisor is \(\boxed{31}\).

📌 Question:** A zoologist tracking nocturnal animal activity cycles notices behavioral patterns recurring every 9 days, prompting interest in numerical periodicity. What is the smallest three-digit number that is divisible by both 9 and 12?

📌 We seek the least three-digit number divisible by \( \text{lcm}(9, 12) \).

📌 First, compute the LCM:

📌 = 3^2, \quad 12 = 2^2 \times 3 \quad \Rightarrow \quad \text{lcm}(9,12) = 2^2 \times 3^2 = 36

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