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Home » Given \( d = 10\sqrt2 \), solve for \( s \): - Crosslake

Given \( d = 10\sqrt2 \), solve for \( s \): - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 5Question: A robotics engineer is programming a modular robot to move in repeating cycles based on motor rotation angles. If the robot rotates in increments that are multiples of $12^\circ$ and $18^\circ$, what is the smallest positive angle (in degrees) that will return the robot to its starting orientation?

📌 Solution: To determine the smallest positive angle at which the robot returns to its original orientation, we must find the least common multiple (LCM) of the two rotation increments, $12^\circ$ and $18^\circ$. First, factor both numbers:

📌 = 2^2 \cdot 3, \quad 18 = 2 \cdot 3^2

📌 The LCM is obtained by taking the highest powers of all prime factors:

📌 \text{LCM}(12, 18) = 2^2 \cdot 3^2 = 4 \cdot 9 = 36

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