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📰 Thus, the sum of all distinct rotational symmetries is $ \boxed{1980^\circ} $. 📰 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) $: 📰 Juan Soto Contract 8101867 📰 Kentucky Distilleries Collapsing Mass Shutdowns Trigger A Spiraling Crisis You Cant Ignore 4526600 📰 You Wont Believe What Lurks Inside These Mythical Ocean Lakes 5588884 📰 Cheapest Flight To 2150514 📰 Unleash The 5E Feats That Defy Belieffeasts Your Eyes And Mind 323156 📰 This Tv Guide App Will Mega Simplify Your Viewing Never Miss A Show Again 3702461 📰 Soylent Green Food 9663163 📰 Wells Fargo In Fort Mohave Az 6495011 📰 Iphone 14 Pro Screen Size 8749787 📰 Circumscribed 6105264 📰 Loan For Construction Of Commercial Property 3864436 📰 I Lost My Mind In The Most Embarrassing Terrifying Way Ever 2813196 📰 Its The Breath In Our Lungs 1922682 📰 Wingo Wingo 1692031 📰 Aizen Bleach Hack Why Experts Are Raging Over Its Shocking Transformation Power 694255