10y^2+40y, 5y^2+45y+100

Question

I am trying ti find the LCD  of these two equations.

Answer 1

Both expressions have the common factor 5, so we divide both by 5:

2y²+8y, y²+9y+20.

2y²+8y=2y(y+4), y²+9y+20=(y+4)(y+5), so they also have y+4 as a common factor. Therefore the highest common factor is 5(y+4). The LCD is 10y(y+4)(y+5) because it includes the HCF and the other factors from each expression. 10y²+40y goes into it y+5 times, and 5y²+45y+100 goes into it 2y times.