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May 17, 2026

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📌 A robotics engineer is programming a robot to perform a series of tasks. The robot completes a task every 6 minutes, 10 minutes, and 15 minutes for three different tasks respectively, starting at the same time. How many minutes will pass before the robot completes all three tasks simultaneously again?

📌 To determine when the robot completes all three tasks simultaneously, we need to find the least common multiple (LCM) of the task intervals: 6, 10, and 15 minutes.

📌 First, find the prime factorization of each number:

📌 Next, identify the highest power of each prime number appearing in the factorizations:

📌 The LCM is the product of these highest powers:

📌 Thus, the robot will complete all three tasks simultaneously every 30 minutes.

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