Question

Holiday Lights in the Park are up for the season. One set of decorative lights blinks every 25 seconds. Another set blinks every 40 seconds. How many seconds will pass before both light sets blink at the same time?

Answer 1

to find how many seconds will oass for them to blink at the same time we must find the minimun common multiple.

to find the minimum common mutiple we need to decompose both numbers into prime numbers like this

after this we multiply all the factors, without multiplying the ones that are both decomposition, in this case the multiplication will be

`5\cdot5\cdot2\cdot2\cdot2`

we only put 2 fives althought there is one five on the decomposition of 40

after that we find that

`\begin{gathered} mcm.(25,40)=5\cdot5\cdot2\cdot2\cdot2 \\ m\mathrm{}c\mathrm{}m\mathrm{}(25,40)=200 \end{gathered}`

200 seconds have to pass in order for the lights to blink at the same time