Question

An electronic device makes a beep after every $60$ seconds. Another device makes a beep after every $62$ seconds. They beeped together at $10\,{\text{A}}{\text{.M}}$ . At what time will they beep together at the earliest $?$

Answer 1

Hint: In this question we have been asked to find the time at which the electronic devices beep together. So, for this we will find a number which is a common multiple of $60$ seconds and $62$ seconds. Therefore, from the discussion we should have the idea that we have to find out the L.C.M of $60$ seconds and $62$ seconds.

Complete step-by-step answer:
The first electronic device makes a beep after every $60$ seconds and the second device makes a beep after every $62$ seconds.
Now, to find at what time the first device and the second device beep together we will find out the L.C.M of $60$ seconds and $62$ seconds because it will give the least time at which these two electronics devices beep together.
Now L.C.M of \[62\] and $60$ is $1860$
Therefore, we found that at the interval of $1860$ seconds both the electronic devices beep together.
Now, convert $1860$ seconds into minutes by dividing $1860$ with $60$
$ \Rightarrow \dfrac{{1860}}{{60}} = 31$
Therefore, at the interval of $31\,{\text{minutes}}$both the electronics devices beep together.
Hence, we can say that the electronics devices will again beep at $10.31\,{\text{A}}{\text{.M}}{\text{.}}$

Note: In this question the important thing is that the students should get the idea that in order to find the time at which the devices will beep together we have to find the L.C.M of the time interval given to us in the question because in this question we are asked to find the common interval at which the two devices will beep together and L.C.M is least common multiple.