No; there is a physical incompatibility between LGA 1156 and LGA 1155.
From Wikipedia:
Processors for LGA 1155 and LGA 1156 sockets are not compatible with each other since they have different socket notches.
I have just bought a core i3 first generation(Intel® Core™ i3-530 Processor (4M Cache, 2.93 GHz Socket LGA1156
) but I looked up the website of the motherboard(H61M-K ASUS) and it showed me this:-
Intel® Socket 1155 for 3rd/2nd Generation Core™ i7/Core™ i5/Core™ i3/Pentium®/Celeron® Processors Supports Intel® 22 nm CPU Supports Intel® 32 nm CPU Supports Intel® Turbo Boost Technology 2.0 Supports CPU up to 77 W
it says it can support 1155 socket core i3 2nd/3rd generation but mine is 1156 core i3 1st generation. Will the processor work?
No; there is a physical incompatibility between LGA 1156 and LGA 1155.
From Wikipedia:
Processors for LGA 1155 and LGA 1156 sockets are not compatible with each other since they have different socket notches.