Puzzle ZAMH 

Workings

Hint
Try starting with the cube root of the number.

Answer
9 x 11 x 13.

Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 1,287, which is roughly 10.88.

Let's try dividing by the closest odd number to 10.88:

   1287 ÷ 11 = 117

We're now after whole divisors of 117, so trying either odd number either side of 11 might work.

Trying either 9 or 13 gives the answer.

Double-Checking
   9 x 11 x 13 = 1,287

Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.