A red string of holiday lights blinks once every 3 seconds, while a string of blue lights blinks once ever 4 seconds. How many times will both sets of lights blink at the same time in 1 minute?

Question

Mathematics

Clayton Rivera

25 January, 23:56

A red string of holiday lights blinks once every 3 seconds, while a string of blue lights blinks once ever 4 seconds. How many times will both sets of lights blink at the same time in 1 minute?

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Esther Castaneda · Answer 1

So both start at 0: It will blink 3 seconds later then again at 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 That's 20 times.

Now for the blues: 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 That's 15 times.

The blink the at the same time at 0 12 24 36 48 and 60

Now here's the thing you should notice The Lowest common multiple of 3 an 4 is 12. So it is no accident that the lights blink every 12th second.