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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) $: 📰 Brian Moynihan Boa 📰 Investigation Begins The Game Hardest And It Leaves Everyone Stunned 📰 Free Admin Gearwall 7649955 📰 Game Studios Careers 📰 Why 22 Hours Spent Counting Every Second Changes Everything 5065287 📰 From Humble Beginnings To Massive Successdiscover The Origin Game That Changed Everything 5005024 📰 Tarjeta Credito Bank Of America 📰 Fidelity 529 Phone Number Your Secret Weapon For Smarter College Funding 9052984 📰 Diner Chain Iconic Location Closure 📰 Finally How To Buy Stocks Without A Brokerstop Missing Out 6543406 📰 The Truth About Tucsons Best Kept Secrets No Guide Ever Spoke 6942853 📰 Dc Subway Map Like Never Before Decoding The System Like A Pro 3063641 📰 Could You Win Big With The Dc Listlottery Try It Before Time Runs Out 2112429 📰 Tribal Payday Loans For Bad Credit Unlock Fast Cash When You Need It Most 2843366 📰 Big Update One Piece Rpg And The Situation Worsens