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Let's dive into a DC Comics themed math problem using the least common multiple (LCM) concept. **Problem:** Batman has 12 Bat-Signals to repair in Gotham City, and each signal requires 4 hours to fix. Meanwhile, Superman has 8 Kryptonian devices to calibrate in Metropolis, and each device takes 6 hours to adjust. If they start working on their tasks at the same time, when will they both finish their work? **Concepts involved:** Least Common Multiple (LCM), Multiples, Factors **Step-by-Step Solution:** 1. **Identify the time periods:** Batman takes 4 hours to repair each signal, so he works in 4-hour blocks. Superman takes 6 hours to calibrate each device, so he works in 6-hour blocks. 2. **Find the least common multiple (LCM) of 4 and 6:** To find the LCM, we need to list the multiples of each number: * Multiples of 4: 4, 8, 12, 16, 20, ... * Multiples of 6: 6, 12, 18, 24, 30, ... The first number that appears in both lists is 12, so the LCM of 4 and 6 is 12. 3. **Determine the time when both will finish:** Since Batman works in 4-hour blocks and the LCM is 12, he will finish all 12 signals in 12 / 4 = 3 blocks, which is 3 × 4 = 12 hours. Similarly, Superman will finish all 8 devices in 12 / 6 = 2 blocks, which is also 2 × 6 = 12 hours. 4. **Verify the solution:** Both Batman and Superman will finish their tasks in 12 hours. To confirm, we can check that Batman will have completed 12 / 4 = 3 blocks of 4 hours each, and Superman will have completed 12 / 6 = 2 blocks of 6 hours each. **Final Answer:** Batman and Superman will both finish their work in 12 hours. How's that? Do you have any questions about this problem or would you like to explore more math adventures with DC Comics characters?

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