what's the LCM of: 2r-1 , r+4

They have no common factors so

(2r-1)(r+4) = 2 r^2 + 7 r - 4

To find the Least Common Multiple (LCM) of two expressions, we'll start by simplifying them as much as possible.

The expressions provided are 2r - 1 and r + 4.

To find the LCM, we first need to factorize the expressions. However, these two expressions cannot be factored further since they don't share any common factors other than 1.

Now, we can proceed to find the LCM. The LCM is the smallest multiple that both expressions share. To determine this, we can use the product of the expressions divided by their greatest common divisor (GCD).

The GCD between 2r - 1 and r + 4 can be found by equating both expressions to zero and solving for r. However, in this case, the GCD is not necessary since we already know that the two expressions don't share any common factors other than 1.

Thus, the LCM of 2r - 1 and r + 4 is found by multiplying the two expressions together:

LCM = (2r - 1) × (r + 4)

That is the final answer for the LCM.