You can speed up your Android devices without cleaning utilities since a native feature is provided in Android operating systems to clear background running apps that consume system resources and cause lags once memory is filled up. Although all those cleaning utilities available for Android can automate this process by regularly cleaning the memory and killing background processes that consume a lot of CPU resources, why not do this manually in case you are not a fan of such apps or you want to make space for other apps, games and files.
Your device has got Recent Apps button pressing which will open all recent apps running in background. You can indivdually swipe apps left or right to remove them from memory or simply press graphical Clear button to clean all background apps. This button varies from device to device. It could be simply “Clear” or “Clear all” text or a button with brush or bin symbol.
Recent apps button on phone got symbols like this:
Background apps which you can clear one by one by swiping left or right or hit the button to remove them all:
Note that there are several apps that automatically restart to synchronize data from internet even if you stop them for example email clients, browsers, cloud apps, games etc. There are options in Power management provided by phone manufacturers to forbid them from starting automatically. You can take advantage of these options to manage automatically starting apps. Please check your phone settings to see if any such options are provided.