Why do some western countries have prison sentences for hundreds of years

Because they don't allow the death penalty, they add up all kinds of crimes, one by one, for hundreds of years.

In some cases, life imprisonment does not have the meaning of "life imprisonment", for example, through commutation of sentence, parole, criminals may only need one or two decades to regain their freedom, to use such a penalty to replace the original application of the death penalty, particularly serious crimes, is not appropriate. Britain and the United States and other countries for the maximum term of imprisonment for a number of crimes, the principle of absolute addition, well between life and imprisonment, the formation of a reasonable penalty ladder, to avoid an imbalance in the penalty system.