Question

Find the LCM of k2 + 6k + 5 and 4k2 + 32k + 60.

Answer 1

The expressions are given below as

`k^2+6k+5,4k^2+32k+60`

Step 1:

Factorise the first expression below

`\begin{gathered} k^2+6k+5 \\ k^2+k+5k+5 \\ k(k+1)+5(k+1) \\ (k+1)(k+5) \end{gathered}`

Step 2:

Factorise the second expression below

`\begin{gathered} 4k^2+32k+60 \\ 4(k^2+8k+15) \\ 4(k^2+3k+5k+15) \\ 4(k(k+3)+5(k+3)) \\ 4((k+3)(k+5) \end{gathered}`

Step 3:

Combine the common factors to get the L.C.M

Therefore,

The L.C.M will be

`4(k+1)(k+5)(k+3)`