Well, the JVM memory model works something like this: values are stored on one pile of memory stack and objects are stored on another pile of memory called the heap. The garbage collector looks for garbage by looking at a list of objects you've made and seeing which ones aren't pointed at by anything. This is where setting an object to null comes in; all nonprimitive (think of classes) variables are really references that point to the object on the stack, so by setting the reference you have to null the garbage collector can see that there's nothing else pointing at the object and it can decide to garbage collect it. All Java objects are stored on the heap so they can be seen and collected by the garbage collector.
Nonprimitive (ints, chars, doubles, those sort of things) values, however, aren't stored on the heap. They're created and stored temporarily as they're needed and there's not much you can do there, but thankfully the compilers nowadays are really efficient and will avoid needed to store them on the JVM stack unless they absolutely need to.
On a bytecode level, that's basically how it works. The JVM is based on a stack-based machine, with a couple instructions to create allocate objects on the heap as well, and a ton of instructions to manipulate, push and pop values, off the stack. Local variables are stored on the stack, allocated variables on the heap.* These are the heap and the stack I'm referring to above. Here's a pretty good starting point if you want to get into the nitty gritty details.
In the resulting compiled code, there's a bit of leeway in terms of implementing the heap and stack. Allocation's implemented as allocation, there's really not a way around doing so. Thus the virtual machine heap becomes an actual heap, and allocations in the bytecode are allocations in actual memory. But you can get around using a stack to some extent, since instead of storing the values on a stack (and accessing a ton of memory), you can stored them on registers on the CPU which can be up to a hundred times (maybe even a thousand) faster than storing it on memory. But there's cases where this isn't possible (look up register spilling for one example of when this may happen), and using a stack to implement a stack kind of makes a lot of sense.
And quite frankly in your case a few integers probably won't matter. The compiler will probably optimize them out by itself in this case anyways. Optimization should always happen after you get it running and notice it's a tad slower than you'd prefer it to be. Worry about making simple, elegant, working code first then later make it fast (and hopefully) simple, elegant, working code.
Java's actually very nicely made so that you shouldn't have to worry about nulling variables very often. Whenever you stop needing to use something, it will usually incidentally be disappearing from the scope of your program (and thus becoming eligible for garbage collection). So I guess the real lesson here is to use local variables as often as you can.
*There's also a constant pool, a local variable pool, and a couple other things in memory but you have close to no control over the size of those things and I want to keep this fairly simple.