Question

Three electronic devices make a beep after every 48 sec, 72 sec and 108 sec respectively. they beeped together at 10
a.m. the time when they will next make a beep together at the earliest is

Answer 1

The earliest time when they deep together is after 3.6 minute it mean 10:3:6 am

Answer 2

Answer:

They will next make a beep together at the earliest is 10:07:02 am.

Step-by-step explanation:

Given : Three electronic devices make a beep after every 48 sec, 72 sec and 108 sec respectively.

To find : They beeped together at 10  a.m. the time when they will next make a beep together at the earliest is?

Solution :

First we find the least common multiple of the three electronic devices.

LCM of 48,72,108 is

$48=2\times 2 \times 2 \times 2 \times3$

$72=2\times 2 \times 2 \times 3\times3$

$108=2\times 2 \times 3 \times 3\times3$

$LCM(48,72,108)=2\times 2 \times 2 \times 2\times3\trimes3\times3$

$LCM(48,72,108)=432$

The least common multiple of 48,72,108 is 432 seconds.

Converting seconds into minutes

$1 s=\frac{1}{60}min$

$432 s=\frac{432}{60}\text{ min}$

$432 s=7.2\text{ min}$

They beeped together at 10  a.m.

They will next make a beep together at the earliest is 10:07:02 am.

i.e. After 10 o'clock 7 minutes and 2 seconds it beep.