Question

LCM of polynomials

9(x+2)(2x-1) and 3(x+2)

Answer 1

To get the LCM of polynomioals or of numbers, you need to first list the prime factors of the polynomials or numbers. In this case you already have the factors since both polynomials are factored out.
The LCM is the product of all factors that are common to both polynomials (or numbers) and factors that are not common to both polynolmials (or numbers) and with the higher exponent.

Here is an example with numbers.
What is LCM of 12 and 30
12 = 2*2*3 = 2^2 * 3
30 = 2 * 3 * 5
The common factors are 2 and 3, but with 2 there is 2^2 and plain 2, so choose higher exponent, 2^2
The 3 is common to both, so choose 3 also.
The 5 is not common since only 30 has it, but choose it too.
Since we chose factors 2^2, 3 and 5, now we multiply them together:
LCM = 2^2 * 3 * 5 = 60

Now with your polynomials it's a similar process.
9(x+2)(2x-1)= 3^2(x + 2)(2x - 1)
3(x+2) = 3(x + 2)
The 3 is common to both, so choose the one with the higher exponent: 3^2
The factor (x + 2) is common to both, so use it too.
Finally, the factor (2x - 1) is not common to both since only one polynomial has it, but you use it too.
LCM = 3^2(x + 2)(2x - 1)
LCM = 9(x + 2)(2x - 1)