Charged multihadron systems in lattice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>QCD</mml:mi><mml:mo>+</mml:mo><mml:mi>QED</mml:mi></mml:mrow></mml:math>

Systems with the quantum numbers of up to 12 charged and neutral pseudoscalar mesons, as well as one-, two-, and three-nucleon systems, are studied using dynamical lattice quantum chromodynamics and quantum electrodynamics ($\mathrm{QCD}+\mathrm{QED}$) calculations and effective field theory. QED effects on hadronic interactions are determined by comparing systems of charged and neutral hadrons after tuning the quark masses to remove strong isospin breaking effects. A nonrelativistic effective field theory, which perturbatively includes finite-volume Coulomb effects, is analyzed for systems of multiple charged hadrons and found to accurately reproduce the lattice $\mathrm{QCD}+\mathrm{QED}$ results. QED effects on charged multihadron systems beyond Coulomb photon exchange are determined by comparing the two- and three-body interaction parameters extracted from the lattice $\mathrm{QCD}+\mathrm{QED}$ results for charged and neutral multihadron systems.