In this work, we calculate the sensitivities on the gauge-boson couplings gaZZ, gaZγ, and gaWW of an axion-like particle (ALP) that one can achieve at the LHC with s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 14 TeV and integrated luminosities of 300 fb−1 (current run) and 3000 fb−1 (High-Luminosity LHC). We focus on the associated production processes pp → Za → (l+l−)(γγ) and pp → W±a → (l±ν)(γγ). We show that better sensitivities on these gauge couplings can be achieved at the LHC for Ma = 1 – 100 GeV, down to the level of 10−4 GeV−1. In conclusion, this study emphasizes the significance of the investigated channels in constraining the ALP couplings at the LHC, offering valuable insights for future experiments dedicated to ALP detection.