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📰 Question: A middle school student is building a robot with gears. One gear rotates 48 times per minute, and another rotates 72 times per minute. If both gears start aligned, after how many minutes will they align again? 📰 Solution: To find when the gears align again, we compute the least common multiple (LCM) of their rotation periods. Since they rotate at 48 and 72 rpm (rotations per minute), the time until alignment is the time it takes for each to complete a whole number of rotations such that both return to start simultaneously. This is equivalent to the LCM of the number of rotations per minute in terms of cycle time. First, find the LCM of the rotation counts over time or convert to cycle periods: The time for one rotation is $ \frac{1}{48} $ minutes and $ \frac{1}{72} $ minutes. So we find $ \mathrm{LCM}\left(\frac{1}{48}, \frac{1}{72}\right) = \frac{1}{\mathrm{GCD}(48, 72)} $. Compute $ \mathrm{GCD}(48, 72) $: 📰 Prime factorization: $ 48 = 2^4 \cdot 3 $, $ 72 = 2^3 \cdot 3^2 $, so $ \mathrm{GCD} = 2^3 \cdot 3 = 24 $. 📰 Hdmi Splitter 2043929 📰 The Dow Future 📰 Reset My Phone 5312290 📰 Unable To Join The Fortnite Login Queue 📰 Plane Crashes Over Philly Firestreams Fill The Sky In Disturbing Crash 7097011 📰 Roblox Not Sending Password Reset Email 7726815 📰 Moth Pokemon 532454 📰 Verizon Orland Park Il 📰 Pokmon Z Reviews That Are Getting Millions Of Views Are You Missing Out 7975910 📰 Yahoo Finance Mdt 📰 Is The Nintendo Switch 2 Worth It Survival Prices Droppedheres What You Need To Know 4110494 📰 Report Reveals Add A Column Excel And The Impact Is Huge 📰 Sentinel One Stock 5450434 📰 Louisiana Lafayette Football 2494463 📰 How Hipaa Security Rule Standards Could Protect Your Dataor Land Your Company In Legal Hot Water 7887012