Solution:
The expressions are given below as
[tex]k^2+6k+5,4k^2+32k+60[/tex]Step 1:
Factorise the first expression below
[tex]\begin{gathered} k^2+6k+5 \\ k^2+k+5k+5 \\ k(k+1)+5(k+1) \\ (k+1)(k+5) \end{gathered}[/tex]Step 2:
Factorise the second expression below
[tex]\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}[/tex]Step 3:
Combine the common factors to get the L.C.M
Therefore,
The L.C.M will be
[tex]4(k+1)(k+5)(k+3)[/tex]