A group of $25$ friends were discussing a large positive integer. The first friend said, "It can be divided by $1$." The second friend said, "It can be divided by $2$." The third friend said, "And by $3$." The fourth friend added, "And by $4$." This pattern continued until everyone had made such a comment. If exactly $2$ friends were incorrect, and those two friends said consecutive numbers, what was the least possible integer they were discussing?

Let's think step by step and output the final answer within \boxed{}.
user