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Home » We seek the least common multiple (LCM) of 18 and 30. - Sterling Industries

We seek the least common multiple (LCM) of 18 and 30. - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 2k \equiv 2 \pmod{7} \Rightarrow k \equiv 1 \pmod{7}

📌 So $ k = 7m + 1 $, and:

📌 x = 9(7m + 1) - 1 = 63m + 8

📌 We want $ x $ to be a two-digit number:

📌 \leq 63m + 8 \leq 99 \Rightarrow 2 \leq 63m \leq 91 \Rightarrow m = 1 \text{ or } 2

📌 Try $ m = 1 $: $ x = 63(1) + 8 = 71 $

📌 Try $ m = 2 $: $ x = 63(2) + 8 = 134 $ (too large)

📌 Thus, the only two-digit solution is $ \boxed{71} $.

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