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Home » Master Chief’s Height Revealed—Is He Actually Taller Than You Imagine? - ToelettAPP

Master Chief’s Height Revealed—Is He Actually Taller Than You Imagine? - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 d = \frac{2025}{3} = 675

📌 Check: $a = 675$, $b = 1350$, $\gcd(675, 1350) = 675$. Can we do better? Try $m + n = 2$: $d = 2025/2 = 1012.5$, not integer. Next smallest $m + n = 3$ gives $d = 675$. Any larger $m + n$ gives smaller $d$. So the maximum possible $\gcd(a, b)$ is $\boxed{675}$.

📌 Question: A paleobotanist studying ancient plant symmetry observes that a fossilized fern has a repeating pattern every $n$ fronds, where $n$ is the smallest three-digit number divisible by both 12 and 18. What is $n$?

📌 Solution: We seek the smallest three-digit number divisible by both 12 and 18, i.e., their least common multiple.

📌 $12 = 2^2 \cdot 3$, $18 = 2 \cdot 3^2$, so:

📌 \mathrm{LCM}(12, 18) = 2^2 \cdot 3^2 = 4 \cdot 9 = 36

📌 Now find the smallest three-digit multiple of 36. Divide 100 by 36:

📌 \div 36 \approx 2.78

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