  We study $\Theta^+(1540)$ productions in kaon-nucleon ($KN$) and
nucleon-nucleon ($NN$) interactions by assuming that the $\Theta^+$ is an
isosinglet with $J^P = \frac12^+$. Possible $t$-channel diagrams with $K^*$
exchange are considered in both reactions as well as $K$ exchange in $NN$
reaction. The cross section for $np \to \Lambda^0 \Theta^+$, which has not been
considered in previous calculations, is found to be about a factor of 5 larger
than that for $np \to \Sigma^0 \Theta^+$ due to the large coupling of
$KN\Lambda$ interaction. The cross sections are obtained by setting
$g_{KN\Theta}^{}=1$ and varying the ratio of
$g_{K^*N\Theta}^{}/g_{KN\Theta}^{}$ so that future experimental data can be
used to estimate these couplings. We also find that the isospin relations hold
for these reactions.
