Question
Four bells start ringing together at 9:00 am. They ring at intervals of 15 seconds, 20 seconds, 30 seconds, and 40 seconds. At what time will they ring together again?
Solution
ATQ,
All the four bells ring together at 9:00 am, and after that, they ring at different intervals. The time after which they will ring together again is the LCM of [15, 20, 30, 40].
15 = 3¹ × 5¹ 20 = 2² × 5¹ 30 = 2¹ × 3¹ × 5¹ 40 = 2³ × 5¹
So, the required LCM = 2³ × 3¹ × 5¹ = 8 × 3 × 5 = 120 seconds = (120/60) = 2 minutes. So, after 2 minutes from 9:00 am, they will ring together again, i.e., at 9:02 am.
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