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Home » 1, 3, 5, 9, 15, 45 - Sterling Industries

1, 3, 5, 9, 15, 45 - Sterling Industries

📅 April 16, 2026 👤 scraface

Apr 16, 2026

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📌 What two-digit positive integer is three less than a multiple of 7, and also three less than a multiple of 11?** But not.

📌 Perhaps the number is such that $ x \equiv -3 \pmod{7} $, $ x \equiv -3 \pmod{8} $, $ x \equiv -3 \pmod{9} $, same.

📌 But let’s suppose the intended LCM was smaller. Suppose the question meant:

📌 "Three less than a multiple of 5, 6, and 7" — then $ \text{lcm}(5,6,7) = \text{lcm}(5,2\cdot3,7) = 210 $ — still too big.

📌 Try smaller: suppose 7, 8, and 10? LCM(7,8,10)=280 — no.

📌 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 $.

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