What is the smallest integer greater than 1 that 1 that leaves a remainder 1 when divided by any of the integers 5 7 8

It would be 281. 280 is divisible by 5, 7, and 8, which can be found by multiplying them all together. you don't need to worry about there being a lower common multiple, and 5,7, and 8 are relatively prime with each other, meaning they share no factors. adding 1 accounts for the remainder of 1.