A scientist recieves signals from three quasars $($distant sources of radio energy$).$ the first quasar sends signals every $84$ seconds, the second quasar every $42$ seconds, and the third quasar every $30$ seconds. A$.$ The scientist wishes to divide each of the three$-$time intervals into the largest possible equal$-$size parts so that these parts are equal for all three$-$time intervals. What is the size of these parts? B$.$ If all three signals are received at the same moment, what is the shorest length of time from that moment before two of the signals will again be received at the same time?