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