Question 45
Five numbers $1$, $2$, $3$, $4$, $5$ are written on a blackboard. A student may erase any two of the numbers $a$ and $b$ on the board and write the numbers $a+b$ and $ab$ replacing them. If this operation is repeatedly performed, can the numbers $21$, $27$, $64$, $180$, $540$ ever appear on the board at the same time?