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📰 Thus, the LCM of the periods is $ \frac{1}{24} $ minutes? No — correct interpretation: The time until alignment is the least $ t $ such that $ 48t $ and $ 72t $ are both integers and the angular positions coincide. Actually, the alignment occurs at $ t $ where $ 48t \equiv 0 \pmod{360} $ and $ 72t \equiv 0 \pmod{360} $ in degrees per rotation. Since each full rotation is 360°, we want smallest $ t $ such that $ 48t \cdot \frac{360}{360} = 48t $ is multiple of 360 and same for 72? No — better: The number of rotations completed must be integer, and the alignment occurs when both complete a number of rotations differing by full cycles. The time until both complete whole rotations and are aligned again is $ \frac{360}{\mathrm{GCD}(48, 72)} $ minutes? No — correct formula: For two periodic events with periods $ T_1, T_2 $, time until alignment is $ \mathrm{LCM}(T_1, T_2) $, where $ T_1 = 1/48 $, $ T_2 = 1/72 $. But in terms of complete rotations: Let $ t $ be time. Then $ 48t $ rows per minute — better: Let angular speed be $ 48 \cdot \frac{360}{60} = 288^\circ/\text{sec} $? No — $ 48 $ rpm means 48 full rotations per minute → period per rotation: $ \frac{60}{48} = \frac{5}{4} = 1.25 $ seconds. Similarly, 72 rpm → period $ \frac{5}{12} $ minutes = 25 seconds. Find LCM of 1.25 and 25/12. Write as fractions: $ 1.25 = \frac{5}{4} $, $ \frac{25}{12} $. LCM of fractions: $ \mathrm{LCM}(\frac{a}{b}, \frac{c}{d}) = \frac{\mathrm{LCM}(a, c)}{\mathrm{GCD}(b, d)} $? No — standard: $ \mathrm{LCM}(\frac{m}{n}, \frac{p}{q}) = \frac{\mathrm{LCM}(m, p)}{\mathrm{GCD}(n, q)} $ only in specific cases. Better: time until alignment is $ \frac{\mathrm{LCM}(48, 72)}{48 \cdot 72 / \mathrm{GCD}(48,72)} $? No. 📰 Correct approach: The gear with 48 rotations/min makes a rotation every $ \frac{1}{48} $ minutes. The other every $ \frac{1}{72} $ minutes. They align when both complete integer numbers of rotations and the total time is the same. So $ t $ must satisfy $ t = 48 a = 72 b $ for integers $ a, b $. So $ t = \mathrm{LCM}(48, 72) $. 📰 $ \mathrm{GCD}(48, 72) = 24 $, so $ \mathrm{LCM}(48, 72) = \frac{48 \cdot 72}{24} = 48 \cdot 3 = 144 $. 📰 The Untold Journey Of Christopher Scholtes That No One Dares To Share 8362157 📰 Heres Why The Share Markets Sharp Correction Will Blow Your Mindact Now 5494800 📰 John Dalton Atomic Theory 9371872 📰 Ghostbusters 2016 The Secret Behind The Ghosts Revealedclick To Know 1332886 📰 Deaths St Louis Mo 9252427 📰 Key Alves 8756830 📰 Prigozhin 4069281 📰 Law Enforcement Circumvents Hipaa Heres The Secret Exception No One Talks About 884249 📰 From Zero To Link Master How To Create Hyper Beloved Shares Instantly 2968733 📰 Functionality Meaning 9555748 📰 Samsara Documentary 1975737 📰 Front Door Window Dl Hack Instantly Boost Security And Looks Proven 9180814 📰 Topsters 3 The Revolutionary Tool Thats Taking The World By Storm 6422124 📰 Flights To Seattle Washington 2406042 📰 Echogenic Liver 5954069