Two bells toll at intervals of 15 seconds and 20 seconds. If they toll together

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Question: Two bells toll at intervals of 15 seconds and 20 seconds. If they toll together at 12:00 PM, when will they toll together again? (2023)

Options:

Correct Answer: 12:10 PM

Exam Year: 2023

Solution:

The LCM of 15 and 20 is 60 seconds. Therefore, they will toll together again at 12:01 PM.

Two bells toll at intervals of 15 seconds and 20 seconds. If they toll together at 12:00 PM, when will they toll together again? (2023)

Two bells toll at intervals of 15 seconds and 20 seconds. If they toll together at 12:00 PM, when will they toll together again? (2023)

Step 1: Identify the intervals at which each bell tolls. The first bell tolls every 15 seconds, and the second bell tolls every 20 seconds.
Step 2: To find out when both bells will toll together again, we need to calculate the Least Common Multiple (LCM) of the two intervals (15 seconds and 20 seconds).
Step 3: Find the multiples of 15: 15, 30, 45, 60, 75, ...
Step 4: Find the multiples of 20: 20, 40, 60, 80, ...
Step 5: Look for the smallest number that appears in both lists of multiples. The smallest common multiple is 60 seconds.
Step 6: Since they toll together at 12:00 PM, we add 60 seconds to this time.
Step 7: 60 seconds is equal to 1 minute, so 12:00 PM plus 1 minute is 12:01 PM.
Step 8: Therefore, the two bells will toll together again at 12:01 PM.

Least Common Multiple (LCM) – The LCM is the smallest multiple that is evenly divisible by both numbers, which in this case determines when the two bells will toll together again.
Time Calculation – Understanding how to add time correctly after finding the LCM to determine the next occurrence.