Find the next number in the series $1,2,6,24,\dots$.

Let's analyze the pattern of progression in the given series:
* First term: $1$
* Second term: $1\times 2=2$
* Third term: $2\times 3=6$
* Fourth term: $6\times 4=24$

Following this consecutive multiplication pattern, the next term will be obtained by multiplying the fourth term by $5$:

$$\text{Next number}=24\times 5=120$$

Alternatively, these are the factorial values: $1!,2!,3!,4!,5!$, where $5!=120$.