Question 127153
The factors of {{{y^3 + 8y^2 + 16y}}} are {{{y}}}, {{{(y+4)}}}, and {{{(y+4)}}}.


The factors of {{{y^2 - 8y}}} are {{{y}}}, and {{{(y-8)}}},


Therefore the LCM needs:


1 factor of  {{{y}}}, 
2 factors of {{{(y+4)}}}, and 
1 factor of {{{(y-8)}}}.


{{{y(y+4)(y+4)(y-8)}}} is your LCM.  I'll let you handle the expansion of the expression if you need it in that form.