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📰 Thus, the smallest number of teeth rotations needed for alignment is 72. For the first gear (24 teeth), this corresponds to $72 \div 24 = 3$ rotations, and for the second gear, $72 \div 36 = 2$ rotations. 📰 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 $oxed{3}$. 📰 Report Finds White Distilled Vinegar Rust Removal And People Are Furious 📰 The Ultimate Hair Spa Unlockedsay Goodbye To Dry Strands Forever 6311535 📰 Chelsea Clinton Net Worth 📰 Power Tip Double Space Your Essay With Just One Clicksave Valuable Time 963742 📰 Biotechnology Quotes 📰 Redmagic 10 Pro 📰 How To Have A Lucid Dream 📰 Argentina Steam 📰 Only 500 Per Weekend At This Secret Getaway House Dont Miss It 9328400 📰 Killer Croc 6793055 📰 English Tagalog Dictionary 📰 You Wont Believe How The Mafia Orchestrated That Brutal Murder Mystery 4211230 📰 Free Games Download For Pc Free 9882616 📰 This Nasallang Piercing Hack Will Make Your Recovery Faster Than Ever 7247960 📰 Mlb The Show Pc