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Home » 4! Download These 7 Blessing Images & Kick Off Monday with Heat! - AMAZONAWS

4! Download These 7 Blessing Images & Kick Off Monday with Heat! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Solution: The two gears will realign at their starting position after a time equal to the least common multiple (LCM) of their rotation periods. We compute $ ext{lcm}(18, 30) $.

📌 Factor both numbers:

📌 $ 18 = 2 imes 3^2 $,

📌 $ 30 = 2 imes 3 imes 5 $.

📌 ext{lcm}(18, 30) = 2 imes 3^2 imes 5 = 90.

📌 Thus, they will first align again after $ oxed{90} $ seconds.

📌 Question: In a nanotechnology sensor, signal pulses are emitted every 7 nanoseconds, and calibration checks occur every 13 nanoseconds. If both events start at time zero, what is the smallest positive time in nanoseconds when both events occur simultaneously?

📌 Solution: We seek the smallest positive time $ t $ such that $ t $ is divisible by both 7 and 13 â that is, $ t = ext{lcm}(7, 13) $. Since 7 and 13 are distinct primes, they are coprime and

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