9514 1404 393
Answer:
660 seconds
Step-by-step explanation:
The least common multiple of 45 seconds and 80 seconds is ...
45×80/GCF(45,80) = 45×80/5 = 720
The next change will be 720 seconds after the last one, so 720 -60 = 660 seconds from now.
_____
<em>Additional comment</em>
You can find the least common multiple by looking at the factors of 45 and 80:
The LCM will include one copy of the common factor and all of the unique factors:
LCM(45, 80) = 5×9×16 = 720
You can see that the greatest common factor is 5, and that the LCM is the product (5×9)(5×16) divided by 5:
LCM(a, b) = a×b/GCF(a, b)
It would be equal to 300/100
W=any whole number
D=any number above 0
= [3x3^-2x(-2)^6/2x3^-1x(-2)^5]^2 = 1