Question

A church bell rings every 40 minutes and a clock tower bell ring every 60 minutes. At
12 PM on a day, both the bells rang together. At what time will both the bells ring together
again?

Answer 1

Answer:

2^3 x 3^2 minutes is the cycle after which they'll ring together. So, 10:12 AM, 11:24 AM and so forth.

Why? You need calculationg the least common multiple. You find the smallest prime factors for each number (24 = 2 x 2 x 2 x 3, hence 2 to the 3rd power x 3; 36 = 2 x 2 x 3 x 3, hence 2^2 x 3^2), then choose ONCE each factor; where the factor appears more than once, you choose the one with the highest power. So, 2^3 (higher power than 2^2 from 36) times 3^2 (higher power than 3^1 from 24).

2^3 x 3^2 = 8 x 9 = 72 minutes, or 1h12′.

Step-by-step explanation:

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