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Home » المحيط = 4 * الضلع = 4 * 12 = 48 م. - Ready Digital AB

المحيط = 4 * الضلع = 4 * 12 = 48 م. - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 Find smallest θ such that θ = 18n, θ = 45k, and θ mod 90 ≠ 0.

📌 So 18n = 45k → 2n = 5k → n = 5m, k = 2m → θ = 18×5m = 90m° → always multiple of 90!

📌 So every multiple of 18° that is also multiple of 45 must be multiple of LCM(18,45).

📌 LCM(18,45) = (18×45)/gcd(18,45) = 810 / 9 = 90.

📌 So the only positions that are multiples of both 18 and 45 are multiples of 90°.

📌 Thus, no non-zero multiple of 18° that is also a multiple of 45° is not divisible by 90? No — LCM is 90, so smallest common multiple is 90°.

📌 But 18n = 90 → n = 5 → 90° → multiple of 90 → invalid.

📌 Next: 180 → n=10 → invalid.

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