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Home » Thus, \( n = 32 \) is the smallest such integer. - DevRocket

Thus, \( n = 32 \) is the smallest such integer. - DevRocket

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Wait — maybe it’s not LCM, but that $ x + 3 $ is divisible by **at least one** of 7,8,9? But that would be and/or, not and.

📌 The key is: three less than a multiple of 7, 8, and 9 — standard interpretation: $ x + 3 $ divisible by all three → divisible by LCM.

📌 So $ x = 504k - 3 $.

📌 Smallest positive: 501 — not two-digit.

📌 Thus, **no such two-digit integer exists**.

📌 But since olympiad problems usually have a solution, perhaps we re-express:

📌 Maybe the question meant: ‘three less than a multiple of 7’, ‘three less than a multiple of 8’, and ‘three less than a multiple of 9’ — but again, same.

📌 Unless a multiple of 7, 8, and 9 means a common multiple, so $ x + 3 = \text{LCM}(7,8,9) = 504 $, $ x = 501 $.

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