--------ASIDE----------------------
There's a nice rule that says:
(greatest common divisor of x and y)(least common multiple of x and y) = xy
Example: x = 10 and y = 15
Greatest common divisor of 10 and 15 = 5
Least common multiple of 10 and 15 = 30
Notice that these values satisfy the above rule, since (5)(30) = (10)(15)
--------BACK TO THE QUESTION! ----------------------

In this question, we can write: (greatest common divisor of 51 and 288)(least common multiple of 51 and 288) = (51)(288)

We're told that the greatest common divisor of 51 and 288 is 3.
So, we get: (3)(least common multiple of 51 and 288) = (51)(288)
Divide both sides of the equation by 3 to get: least common multiple of 51 and 288 = (51)(288)/3 = 4896

Answer: 4896