n = 15 → 270° → 270 ÷ 90 = 3 → invalid.
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- We need 18n = multiple of 45 → n divisible by 5/ gcd(2,5)=5 → n multiple of 5? Actually: 18n divisible by 45 → n divisible by 45 / gcd(18,45) = 45/9 = 5 → yes, n divisible by 5.
- So smallest n = 5 → angle = 18×5 = 90° → multiple of 90 → invalid.
- Next: n = 10 → 180° → multiple of 90 → invalid.
- n = 20 → 360° → 360 ÷ 90 = 4 → invalid.
- But 45° is target, and no integer n gives 18n = 45 → so 45° is unreachable in 18° steps?
- Wait — the arm rotates incrementally, so position must be exact. But 45 and 18 have LCM:
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