The three consecutive integers can be written as:

x-1, x and x+1, where x is integer.

x - 1 is the smallest integer of the the three.

The sum of three consecutive integers is 21 larger than twice the smallest integer:

(x - 1) + x + (x + 1) = 21 + 2(x - 1)

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click here to see the equation solved for x

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x = 19

x - 1 = 19 - 1 = 18

19 + 1 = 20

The three integers are 18, 19 and 20.