In an industrial area three factories give out sirens at an interval of 40 min, 1 hour anf 1 and a half hour. respectively. Find the time between the two simultaneously sounds of three sirens.
6 hrs
Find the LCM of 40 , 60 and 90 then divide the answer by 60
Ans: 6
To find the time between two simultaneous sounds of the three sirens, we need to find the time at which all three sirens go off at the same time.
First, let's find the time taken by each siren to complete one cycle.
Siren 1: Interval = 40 minutes between each sound
Siren 2: Interval = 1 hour between each sound
Siren 3: Interval = 1 and a half hours between each sound
To find the time taken for each siren to complete one cycle, we need to find the least common multiple (LCM) of the three intervals.
LCM(40, 60, 90):
Step 1: Find the prime factors of each number:
40 = 2 * 2 * 2 * 5
60 = 2 * 2 * 3 * 5
90 = 2 * 3 * 3 * 5
Step 2: Take the highest power of each prime factor:
2^3 * 3^2 * 5 = 360
The LCM of 40, 60, and 90 is 360 minutes.
So, all three sirens will go off simultaneously every 360 minutes.
Therefore, the time between two simultaneous sounds of the three sirens is 360 minutes.