Answer :
Answer: 210
Step-by-step explanation:
This question is about LCM.
We are finding the same time for all 3 light flashes.
Light A: 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,195,200,205,210
Light B: 6,12,18,24,30,36,42,48,54,60,66,72,78,84,90,96,102,108,114,120,126,132,138,144,150, 156,162,168,174,180,186,192,198,204,210
Light C: 7,14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119,126,133,140,147,154,161,168,175, 182,189,196,203,210
Light A: 42 Light B: 35 Light C: 30
Final answer:
The three lights will flash together 17 times in an hour. This is found by finding the Least Common Multiple (LCM) of the flash frequencies (5, 6, 7 seconds) which is 210 seconds, and dividing the total seconds in an hour (3600 seconds) by 210.
Explanation:
To find out when all three lights flash at the same time, we need to find the Least Common Multiple (LCM) of the three numbers: 5, 6, and 7. The LCM of these numbers is the smallest number that each of them will divide into evenly, which is also the amount of time it will take for all three lights to flash together again.
So, we need to find the Least Common Multiple (LCM) of 5, 6, and 7. By multiplying the three numbers together, we find that the LCM is 210 seconds.
An hour has 3600 seconds (60 minutes * 60 seconds). Therefore, in one hour, the lights will flash together 3600/210 = 17 times.
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