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

Answer:

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

Step-by-step 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

$LCM= (k+1)\times 13(k+1)\times 5k^3(k+4)\\=65k^3(k+1)^2(k+4)$