4 different electronic devices make a beep after every 30 min, 1 hour, 3/2…

To find when the devices will beep together again, we need to determine the Least Common Multiple (LCM) of their individual beeping intervals.

Step-by-Step Calculation
1. Standardize the time intervals (in hours):

Device 1: 30 minutes = 1/2 hour

Device 2: 1 hour = 1 hour

Device 3: 3/2 hours = 1.5 hours

Device 4: 1 hour 45 minutes = 1 hour + 45/60 hours = 1 + 3/4 = 7/4 hours

2. Calculate the LCM of the fractions (1/2, 1/1, 3/2, 7/4):
The rule for the LCM of fractions is: LCM of numerators / HCF of denominators.

Numerators: 1, 1, 3, 7

LCM of 1, 1, 3, 7 = 21

Denominators: 2, 1, 2, 4

HCF of 2, 1, 2, 4 = 1

LCM = 21 / 1 = 21 hours.

3. Determine the next time they beep together:
The devices beeped together at 12 noon. Adding 21 hours to 12 noon:

12 noon + 12 hours = 12 midnight

12 midnight + 9 hours = 9 am the next day.