Question

Find the least common multiple (LCM) of
`13k^2+26k+13` and
`5k^5+25k^4+20k^3`. You can give your answer in its factored form.

Answer 1

`LCM=65k^3(k+1)^2(k+4)`

Explanation:

We are given the following:

`13k^2 + 26k +13`

`5k^5 + 25k^4+20k^3`

We can factor the given polynomial in the following manner.

`13k^2 + 26k +13\\= 13(k^2 + 2k +1)\\=13(k+1)^2`

`5k^5 + 25k^4+20k^3\\=5k^3(k^2 + 5k + 4)\\=5k^3(k\left(k+1\right)+4\left(k+1\right))\\=5k^3(k+1)(k+4)`

Thus, the common factors of the both polynomials are:

(k+1)

Thus, the LCM of both the polynomials is

`LCM= (k+1)* 13(k+1)* 5k^3(k+4)\\=65k^3(k+1)^2(k+4)`