1. The least of three consecutive integers is divided by 10, the next is divided by 17, the greatest is divided by 26 and the sum of the quotients is 10.

Consecutive integers means they are one after the other. For example, 1,2,3 or 7,8,9 are three consecutive intergers.

So if the first integer is x, the second is x + 1 and the third is x + 2.

Of course, the least integer will be the first one, so we have:

x/10 + (x + 1)/17 + (x + 2)/26 = 10

It's kind of hard coming up with the LCD for 10, 17, and 26, so let's just make the LCD the multiple of all of them = 10*17*26 = 4420.

x/10 + (x + 1)/17 + (x + 2)/26 = 10

442x + 260(x + 1) + 170(x + 2)

------------------------------ = 10

.................4420

Now multiply both sides by 4420 to cancel the denomenator:

=> 4426x + 260(x + 1) + 170(x + 2) = 44200

=> 442x + 260x + 260 + 170x + 340 = 44200 ..........expanded the brackets

=> 872x + 600 = 44200

=> 872x = 44200 - 600 = 43600

=> x = 43600/872

=> x = 50

So the three integers are 50, 51, and 52