The　joint　effects　of　an　ac　field　and　intralead　interaction　on　shot　noise　of　a　Kondo　quantum　dot　coupled　to　Luttinger　liquid　leads　is　investigated.　A　general　photon-assisted　zero-frequency　shot　noise　formula　is　derived　by　use　of　the　extended　equation　of　motion　of　the　nonequilibrium　Green　function.　The　photon-assisted　shot　noise　demonstrates　antiresonant-like　behavior.　The　differential　shot　noise　versus　bias　voltage　exhibits　steps　the　widths　of　which　are　just　the　ac　frequency.　With　the　increase　of　the　intralead　interaction,　the　antiresonances　and　step-structure　are　gradually　smoothed　and　eventually　disappear　in　the　limit　of　the　strong　intralead　interaction.　In　the　limit,　the　shot　noise　scales　as　a　power　law　in　bias　voltage,　a　signature　of　strong　intralead　interactions.　The　measurements　of　the　photon-assisted　zero-frequency　shot　noise　can　provide　valuable　information　of　the　intralead　interaction.