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Home » Let the width be \( w \). Then the length is \( 2w + 5 \). - Baxtercollege

Let the width be \( w \). Then the length is \( 2w + 5 \). - Baxtercollege

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 $ 7 $: prime

📌 $ 8 = 2^3 $, $ 9 = 3^2 $ → coprime to others

📌 So $ \text{lcm} = 7 \cdot 8 \cdot 9 = 504 $, correct.

📌 Hence, no two-digit number satisfies $ x \equiv -3 \pmod{504} $.

📌 The smallest positive solution is $ x = 501 $, which is three-digit.

📌 Therefore, there is **no two-digit** such number.

📌 But perhaps the question meant **three less than a multiple of 7, or 8, or 9**, but that would be too weak.

📌 Alternatively, maybe it meant a number such that $ x + 3 $ is divisible by **each** of $ 7, 8, 9 $ individually, but not necessarily simultaneously. But that’s redundant — divisibility by each implies divisibility by their LCM.

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