Ared string of holiday lights blinks once every 3 seconds while a string of blue lgihts blink once every 4 seconds. how many times with both sets of lights blink at the same time in 1 minute

So we want to find the times where they intersect, through their multiples.

For example, the multiples of 3 are 6, 9, 12, etc.

3: 3, 6, 9, 12...

4: 4, 8, 12...

So the least common multiple is 12.

So we know they blink at the same time once every 12 seconds.

Now we just need to find how many times 12 fits into a minute, or 60 seconds.

60 / 12 = 5

So the lights will blink at the same time 5 times in one minute.