If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n ?

The least possible values of n is:

                                   11

We know that the product of first n natural numbers is: n!

Now, we are asked to find the minimum value of n such that n! is a multiple of 990.

This means that:

Now we know that:

Now we know that we obtain all of these factors when n is minimum 11.

Since,

This means that :

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