Question

Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon at what time will they beep again for the first time?

Answer 1

They will beep together after time interval which is multiple of both i.e. 50 and 48.
That means we have to find out the LCM  of 50 and 48.

48=2x2x2x2x3
50=2x5x5
LCM of 48 and 50 is = 2x2x2x2x3x5x5= 1200

so the bell will rang together after 1200 s or 1200/60 minutes = 20 minutes

time = 12:20 pm

Answer 2

Given:

Two-alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds

To Find:

If they first beep together at 12 noon at what time will they beep again for the first time?

Solution:

It is given that they ring at an interval of 50 and 48 seconds respectively and they first beep at 12 noon

so to find when they will beep again we need to find the LCM of the given numbers ( i will be using the Factorization method to find LCM)

$50=2*5*5\\48=2*2*2*2*3\\LCM=2^4*3*5^2\\=1200$

so the LCM is 1200 seconds

which will be 1200/60=20 mins

so the time will be

=12:00+20mins

=12:20 pm

Hence, they will beep again at 12:20 pm.