Question

A string of lights has two blinking lights. One blinks every twelve minutes while the other blinks every forty four minutes. If they both blinked at 1pm, when is the next time they will blink again. (Find the LCM (Least Common Multiple))

Answer 1

They will both blink again at 3:12 pm.

Explanation:

As indicated by the question, the way to solve is to find the Lowest (or Least) Common Multiple of both numbers.

As such:

`\text{List the factors of 12 and 44:}\\12=2*2*3\\44=2*2*11\\\\\text{Take the common factors only once and multiply them by the non-common factors:}\\2*2*3*11=132 \text{ (LCM)}`

Now knowing the LCM is 132, we convert those minutes into hours and minutes:

`(132)/(60)=2(12)/(60) \text{ (2 hours and 12 minutes)}`

Add this to the original time:

`1:00\text{ pm } + \text{ }2:12 \text{ }= \text{ }3:12\text{ pm}`