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The compression-mode isoscalar giant monopole resonance (ISGMR) has been studied in the Sn, Cd and Pb isotopes using inelastic scattering of 400 MeV {alpha}-particles at extreme forward angles, including 0 deg. We have obtained completely 'background-free' inelastic-scattering spectra for the Sn, Cd, and Pb isotopes for a wide angular and excitation-energy range. The various giant resonances excited with different transferred angular momenta were extracted by a multipole-decomposition analysis (MDA). It was found that the centroid energies of the ISGMR in Sn isotopes are significantly lower than the theoretical predictions. The K{sub {tau}} in the empirical expression for the nuclear incompressibility has been determined to be K{sub {tau}} = -550{+-}100 MeV for the Sn isotopes. The extracted value for the Cd isotopes is K{sub {tau}} = -480{+-}100 MeV. These numbers are consistent with values of K{sub {tau}} = -370{+-}120 MeV obtained from an analysis of the isotopic transport ratios in medium-energy heavy-ion reactions, K{sub {tau}} -500{sub -100}{sup +120} MeV obtained from constraints placed by neutron-skin data from anti-protonic atoms across the mass table, and K{sub {tau}} = -500{+-}50 MeV obtained from theoretical calculations using different Skyrme interactions and relativistic mean field (RMF) Lagrangians. Stringent constraints on interactions employed in nuclear structuremore » calculations are obtained on the basis of the experimentally determined values for K{sub {infinity}} and K{sub {tau}}. These parameters constrain as well the equation of state (EOS) of nuclear matter. However, a significant discrepancy still remains. The ISGMR positions in Sn and Cd isotopes are systematically lower than the predictions obtained on basis of determined from the ISGMR in {sup 208}Pb. This raises the question ''Why are Sn and Cd nuclei so soft?''. For a clue to solve the problem, we discuss the preliminary results on the exact positions of the ISGMR in {sup 204,206,208}Pb.« less