  The different ground state energies of N-pion and M-kaon systems for N+M <=12
are studied in lattice QCD. These energies are then used to extract the various
two- and three- body interactions that occur in these systems. Particular
attention is paid to additional thermal states present in the spectrum because
of the finite temporal extent. These calculations are performed using one
ensemble of 2+1 flavor anisotropic lattices with a spatial lattice spacing a_s
~ 0.125 fm, an anisotropy factor {\xi}=a_s/a_t=3.5, and a spatial volume L^3 ~
(2.5 fm)^3. The quark masses used correspond to pion and kaon masses of m_{\pi}
~ 383 MeV and m_K ~ 537 MeV, respectively. The isospin and strangeness chemical
potentials of these systems are found to be in the region where chiral
perturbation theory and hadronic models predict a phase transition between a
pion condensed phase and a kaon condensed phase.
