Question

(C) Four bells toll with intervals 3, 7, 12 and 14 seconds respectively. At a certain time all the 4 bells Rang in the toll together. After how long will they toll together?
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Answer 1

Here

4 bells ring together at 3, 7, 12 and 14 seconds respectively.

Here we need to find the Least Common Multiple because we are finding the least time taken for the bells to ring at common

Finding LCM;

• 3 = 3 × 1
• 7 = 7 × 1
• 12 = 2² × 3
• 14 = 2 × 7

LCM = Product of highest power

→ LCM = 2² × 3 × 7

→ LCM = 4 × 21

→ LCM = 84

Convert 84 seconds to minutes.

84 seconds = 60 + 24 seconds = 1 minute 24 seconds

So, they will toll together after 1 minute 24 seconds