In order to get the LCM of two binomial expressions (5x - 9) and (3x + 8), you need to factor first each binomial if factorable.
In this given binomial expression (5x - 9) and (3x + 8), you do not need to factor both because they are not factorable.
Next thing to do is to multiply the two binomial expressions by using FOIL method.
(5x - 9)(3x + 8) = 15x^2 + 40x - 27x - 72 = 15x^2 + 13x - 72
Therefore, the LCM of (5x - 9) and (3x + 8) is 15x^2 + 13x- 72.
