[en] We explore the inclusive hadroproduction of the D_s_0"∗(2317), D_s_1(2460) and D_s_J(2860) states at the Large Hadron Collider under the assumption that these hadrons are S-wave meson-meson molecules. In addition, the D_s_2(2910), a predicted bound state of the D_2(2460)K system, is also discussed. We first derive a factorisation formula for the production rates based on effective field theory. Then we make use of two MC event generators, Herwig and Pythia, to simulate the production of pairs of charmed mesons and kaons. Using effective field theory to handle the final state interaction among the meson pairs, we give an estimate of the inclusive production rates for these particles at the order-of-magnitude accuracy. Our results show that the cross sections for the pp→D_s_0"∗(2317) and pp→D_s_1(2460) at the LHC are at O(1 μb) level, while the ones for the pp→D_s_J(2860) and the pp→D_s_2(2910) are smaller by about one order of magnitude. Such estimates suggest that these four exotic states could be copiously produced at the LHC. A study of these states at the LHC will thus provide valuable information on hadron spectroscopy as well as hadron interactions