1. A computer program product for selectively clearing a local Translation Lookaside Buffer (TLB) of a processor or a plurality of Translation Lookaside Buffers of a plurality of processors, the computer program product comprising: computer readable storage medium having program code embodied therewith, the program code readable by a computer processor to perform a method comprising: executing, by the processor, an instruction, the executing comprising: determining one or more translation table entry locations specified by the instruction; based on a local-clearing (LC) control specified by the instruction being a first value, selectively clearing TLBs in a plurality of processors in a configuration of entries corresponding to the determined translation table entry location; and based on the local-clearing (LC) control being a second value, selectively clearing only the TLBs of the processor of the configuration executing the instruction of entries corresponding to the determined translation table entry location.