Find the least common multiple (LCM) of the polynomials \(4x^2-9\) and \(2x-3\).

Step 1 ：Step 1: Factorize the given polynomials first. \(4x^2-9\) is a difference of squares and can be factored as \((2x-3)(2x+3)\). The polynomial \(2x-3\) is already in its simplest form.

Step 2 ：Step 2: Identify the greatest common factor (GCF) of the two polynomials. The GCF is \(2x-3\).

Step 3 ：Step 3: Use the relationship between the product of two numbers, their LCM and GCF to find the LCM. If the numbers are a and b, this relationship is given as \(ab = \text{LCM}(a, b) \times \text{GCF}(a, b)\). In this case, the polynomials are \((2x-3)(2x+3)\) and \(2x-3\), and their GCF is \(2x-3\). So, \((2x-3)(2x+3) = \text{LCM}((2x-3)(2x+3), 2x-3) \times (2x-3)\).

Step 4 ：Step 4: Solve the above equation to find the LCM. The LCM is \((2x-3)(2x+3) / (2x-3) = 2x + 3\).