A neon sign flashes every 4 seconds, another neon sign flashes every 6 seconds. If they flash together,how manyseconds later will they flash together again?

Answer 1

You can look at common multiples. The closest one is 12.

0, 4 seconds, 8 seconds, 12 seconds
0, 6 seconds, 12 seconds

If you want to make it more complicated (I'm not sure your skill level or the level of the material) you could find the frequency of each and then the beat frequency is the difference of the two.

The first light has a frequency of 1/4 hz and the second is 1/6 hz (0.25 hz and 0.167 hz)

beat frequency: 0.25-0.167hz = 0.083 hz

this means the flashes line up 0.083 times per second.

to find the period you take the inverse of that frequency:

0.083^-1=12.0482

in other words they line up every 12 seconds.

if the second method is jibberish to you, stick with the first thing. the second method is for more complicated frequencies, like the frequencies of sounds and so on.

Answer 2

You need the LCM (lowest common multiple) of the two numbers.

Here's a systematic way to find the LCM between two numbers.

In the following calculation, the number on the right is a common factor.

Extract a common factor on each line (write on the right). Then divide each number by the common factor and write on a new line. Continue until there are no more common factors.
4 6 | 2
2 3

The LCM is the product of the numbers at the bottom row and ALL the common factors, in this case, the LCM is 2*3*2=12.

For bigger numbers, it works like this:

24 36 | 6
4 6 |2
2 3

The LCM is 2*3*2*6=72