Avery gets newsletters by email . he get one for sports every 5 days, one for model rail rounds every 10 days , and one for music every 8 days. if he got all three today how many more days will it be until he gets all three newsletters on the same day again?

To find when they all meet, we have to find the lowest common multiple (LCM). To do that, we can do a bit of guess and check where we find the multiples of the highest number and see if they're multiples of the other 2. Since 10 is a multiple of 5, we know all multiples of 10 are multiples of 5, so we just have to find when 10 and 8 meet. 10*1=10, which doesn't work. 10*2=20, which doesn't work. Neither does 30, but for 40, 8*5=40 and 10*4=40, proving that all 3 are together every 40 days