9 . . . the square of 3.
The next one is the square of 4 . . . 16 .
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Since a thousand squared is a million, the "smallest..." is the square of 1001, and the "largest..." is the square of 999.
Find 3 consecutive numbers where the product of the smaller two numbers is 19 less than the square of the largest number.
Perfect cubes smaller than 135 are 1, 8, 27, 64, and 125. Of these, 1 and 27 are factors of 135, so 27 is the largest factor of 135 that is a perfect cube.
11,12,13
5040 is not a perfect square. The greatest perfect square less than 5040 is 4900.