Since logical memory maps to the RAM (physical memory) it has be stored somewhere right and it will obviously take large bunch of memory of itself. Where is it stored?
I'm not sure what you mean by "logical memory"...
Memory is usually composed of physical memory and virtual memory. Physical memory is usually RAM, hard drives, solid-state drives, etc. It's the actual chips and stuff you plug into your computer (hence "physical").
However, it would be impractical if a larger scale OS is trying to run various applications at once and we only use this memory in a sequential manner, right? That's where virtual memory and virtual mapping comes into play. It's a matter of optimization used by the OS to improve performance.
"It" isn't exactly "stored" anywhere.
Logical memory is stored in physical memory, and in various places on your hard drive. The usual places are a swap file (stores data from logical memory that has been modified but not used for a while), and memory mapped files. For example, software playing an 8 GB video file may "memory map" that file, which means the logical memory is increased by 8 GB, and those 8 GB are stored in the video file.