Q. 244.6( 8 Votes )

An electronic device makes a deep after every 60 seconds. Another device makes a beep after every 62 seconds. They beeped together at 10 a.m. At what time will they beep together at the earliest?

Answer :

Given: Device 1 beeps after 60 seconds.


Device 2 beeps after 62 seconds.


To find: the time they beep together.


Explanation:


To find the minimum possible value we find LCM.


So, the devices will beep simultaneously at the LCM of intervals of beeps.


So, LCM of 60 and 62 -


Prime factors of the numbers are -


60 = 2 × 2 × 3 × 5


62 = 2 × 31


LCM = product of prime factors with highest powers


= 22 × 3 × 5 × 31


= 1860 seconds


devices will beep simultaneously after 1860 seconds.


We know 1 min = 60 seconds,


So, 1860 seconds = 1860/60 minutes


= 31 minutes.


the next time they will beep simultaneously at 10:31 hrs.


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