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15, 16 or -16, -15

Let x be the first number & then x+1 will be the next number

so,

x*(x+1) = 240

x2+x-240 = 0

Now use the quadratic formula to find the roots: a=1, b=1, c=-240

Doing that the roots the equation are 15, -16

So the two consecutive numbers whose product is 240 is either 15 & 16 or

-16 & -15.

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