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📰 Therefore, the smallest number of full rotations for alignment is $oxed{3}$ rotations for the 24-tooth gear and $oxed{2}$ for the 36-tooth gear, but the alignment occurs at $oxed{72}$ total teeth moved, so the minimal number of full rotations of the *first gear* required is $oxed{3}$. However, the question asks for the smallest number of full rotations each must make to align—this is interpreted as the LCM of their rotation cycles. Since one full rotation of the 24-tooth gear moves 24 teeth, and 72 is the LCM, the first gear rotates $72/24 = oxed{3}$ times, the second $72/36 = oxed{2}$. But the smallest number of full rotations each must make to realign is the LCM cycle completed, so the answer is the LCM of the number of rotations: $3$ rotations for the 24-tooth gear and $2$ for the other. But to match the format—single answer—we interpret as: 📰 The smallest number of full rotations of the **24-tooth gear** required for alignment (so that both complete an integer number of cycles) is $oxed{3}$. 📰 Thus, the final answer is $oxed{3}$. 📰 Does Subway Accept Ebt This Consumers Surprising Discovery Will Change Everything 2427584 📰 Connections March 1 2025 7034270 📰 Cheap Dividend Stocks Under 10 That Are Rewarding Investors With Yield Like A Dream 5896574 📰 Refinance Rate Today 1572597 📰 Front Runner Jdbc Download Driver Instant Save For Smarter Database Work 3689334 📰 How To Make A Private Match Fortnite 9924800 📰 Audi A8L 5480850 📰 How To Restrict Time On Apps 2101416 📰 Endometrin 2623126 📰 Why Everyones Obsessed With Fmlthe Hard Hitting Meaning Behind The Slang 2833281 📰 Shocking Facts Exclusive Clips Exploring Thomas Hadden Churchs Films Series Like A Pro 2576291 📰 Function For Microtubules 7732186 📰 You Wont Believe How Easy It Is To Fix Your Burr Basket Watch Now 7118311 📰 Bridgewater Marriott 1059621 📰 The Ultimate Guide How To Use All Done Sign Language Like A Nativewatch Now 8478962