Wilson theorem states that if n is a prime number that n divides `(n-1)!+1` using this find the smallest divisor of `12!+6!+12!xx6!+1!`.

Explanation

Wilson theorem states that `(n-1)!+1` is divisible by `n`.

Now, `12!+6!+12!xx6! +1! = 12!+12!xx6!+6!+1`

Now, from Wilson theorem, `6!+1` will be divisible by `7`.

`:. 12!+12!xx6!+6!+1` will be divisible by `7` as `12!` and `12!xx6!` are also divisible by `7`.

So, the smallest divisor of the given number is `7`.