Question

Paul coughs every 8 seconds, Karen coughs every 10. If they both cough at the same time, in how many seconds will they both cough together in?

Answer 1

8|2
4|2
2|2
1

10|2
 5|5
 1

$2^3\cdot5=40$

40 seconds

Answer 2

This is also called the LCM or the Least Common Multiple! To find it you have to factor out both numbers:

      8=2*2*2
    10=2       *5   and I made space on purpose because there are no 5's in #8
LCM=2*2*2*5=40 seconds
Looking down from 8 to 10 you see that under first number 2 there is another 2, but under second, and third number 2 there is no other 2's. The first one is going to be written only once even though there are two of them and I even put it in bold so you would notice what I'm talking about.

Hope this helps and if you have any questions let me know!