Find the incorrect number in the following series:
$$1,12,144,1782,20736$$

Let's examine the mathematical pattern of progression between consecutive terms in the series:
* First term = $1$
* Second term = $1\times 12=12$
* Third term = $12\times 12=144$
* Fourth term should be = $144\times 12=1728$

Let's verify the fifth term using the corrected fourth term ($1728$):

* Fifth term = $1728\times 12=20736$

The series consistently multiplies the previous term by $12$. The number $1782$ is incorrect as it deviates from this geometric progression rule. It must be replaced by $1728$.