Solution: The two gears will realign at their starting position after a time equal to the least common multiple (LCM) of their rotation periods. We compute $ ext{lcm}(18, 30) $.
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- So, there are $ 10 imes 4 = 40 $ such plants.
- Thus, the number of plants that exhibit the trait is $ oxed{40} $.
- Question: A mechanical engineer is designing a gear system where one gear rotates every 18 seconds and another every 30 seconds. If both start synchronized, after how many seconds will they first align at the starting position again?
- Factor both numbers:
- $ 18 = 2 imes 3^2 $,
- $ 30 = 2 imes 3 imes 5 $.
