High School

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The "Open" sign at Cenzo's flashes every 4 seconds. The "Open" sign at The Kettle flashes every 5 seconds. The "Welcome" sign at Centrella's Deli flashes every 6 seconds. If the signs are turned on and flash at the same time, how long will it take for them to flash at the same time again?

Answer :

It will take 60 ( one minute) for the signs to flash at the same time


Find the lcm ( least common denominator)
4: 4,8,12,16,20,24,28,32,36,40,44,48,52,
56,60
5: 5,10,15,20,25,30,35,40,45,50,55,60
6: 6,12,18,24,30,36,42,48,54,60

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Rewritten by : Barada

The signs at Cenzo's, The Kettle, and Centrella's Deli will flash at the same time again after 60 seconds.

The "Open" sign at Cenzo's flashes every 4 seconds, the "Open" sign at The Kettle flashes every 5 seconds, and the "Welcome" sign at Centrella's Deli flashes every 6 seconds.

1. First, list the multiples of each interval:

  • Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
  • Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
  • Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...

2. Next, identify the smallest multiple common to all three sets:

  • LCM of 4, 5, and 6 is 60.

Therefore, it will take 60 seconds for all three signs to flash at the same time again.