 A are integers. The tropical year <span class="nowrap">P<sub>s</sub></span> also needs to be expressed in a fraction. There are two ways to do this. The first method was used before the 7th century, in which a <i>zh&#257;ng</i> cycle was specified. A <i>zh&#257;ng</i> cycle is simply the least common multiple of <span class="nowrap">P<sub>L</sub></span> and <span class="nowrap">P<sub>s</sub></span>. Suppose a <i>zh&#257;ng</i> cycle contains p synodic months and q tropical years. Then we have <span class="