Observations of the Large Magellanic Cloud (LMC), particularly in the radio and high-energy gamma-ray range, offer the possibility of understanding the distribution of cosmic rays in a galaxy other than our own and determining the role that these quantities play in galactic dynamic balance. The LMC has the advantage of being our nearest galactic neighbor and of being observed at a not too large an angle to the normal to the plane. The cosmic-ray energy density distribution for the LMC is calculated quantitatively based on the concept of dynamic balance and a scale of coupling between the cosmic rays and matter in a range allowed by present observations. Based on the very slowly varying ratio of the cosmic-ray electron to nucleon energy density ratio with relevant local galactic conditions and the close similarities to our galaxy, the cosmic-ray nucleon density distribution in the LMC is also determined from the cosmic-ray electron density distribution deduced from synchrotron radiation measurements in a manner consistent with dynamic balance. It is seen that within uncertainties there is quantitative agreement between the two for a cosmic-ray, matter coupling scale of about 21/2 kiloparsecs both in terms of magnitude and distribution, thus supporting both the concept of dynamic balance and the galactic origin of the bulk of cosmic rays. Future gamma-ray astronomy measurement above approximately 10(2) MeV will be able to provide a test of this cosmic-ray density distribution for the LMC.