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LUX-ZEPLIN (LZ) is a second-generation direct dark matter experiment with spin-independent WIMP-nucleon scattering sensitivity above 1:4 x 10-48 cm2 for a WIMP mass of 40 GeV/c2 and a 1000 d exposure. LZ achieves this sensitivity through a combination of a large 5:6 t fiducial volume, active inner and outer veto systems, and radio-pure construction using materials with inherently low radioactivity content. The LZ collaboration performed an extensive radioassay campaign over a period of six years to inform material selection for construction and provide an input to the experimental background model against which any possible signal excess may be evaluated. The campaign and its results are described in this paper. We present assays of dust and radon daughters depositing on the surface of components as well as cleanliness controls necessary to maintain background expectations through detector construction and assembly. Finally, examples from the campaign to highlight fixed contaminant radioassays for the LZ photomultiplier tubes, quality control and quality assurance procedures through fabrication, radon emanation measurements of major sub-systems, and bespoke detector systems to assay scintillator are presented.