How do you find the LCM of #k^2-2k-8, (k+2)^2#?
We are given the following algebraic expressions
We need to find the Least Common Multiple (LCM)
To find the LCM, we will use the following steps:
We must express each expression as the product of it's factors. If there are Prime Factors we must use them
We need to find the product of each factor with the highest power that occurs in the expressions
The product from above is our required LCM
Hence, LCM is the smallest expression that is divisible by each of the given algebraic expressions.
Let us first consider
We will break the above expression into appropriate groups as shown below:
Factor Out as shown below:
Hence, we get the factors
Next, we will consider
This can also be written as the product of two factors:
We will now compute an appropriate expression comprising of factors that appear either in
Hence, we get our LCM:
Hope this helps.