A power adjustment circuit includes memory controller logic that is couplable to system memory or other memory if desired. The memory control logic is operative to provide a variable memory clock signal to the system memory and to place the system memory in a self refresh mode wherein the self refresh mode does not require a memory clock signal. Thereafter, the memory clock control logic adjusts the frequency of the memory clock signal to a lower (or higher) frequency clock signal, and in response to the frequency of the memory clock signal becoming stable, the memory clock control logic restores the memory to a normal mode using the lower adjusted frequency memory clock signal. As such, a dynamic memory clock switching mechanism is employed for quickly varying the frequency of memory modules for discrete graphics processors, graphics processors integrated on a chip, or any other processors such that the memory clock can be reduced to a lower frequency in real time to save power.