Respuesta :

Answer:

The least possible values of n is:

                                   11

Step-by-step explanation:

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:

[tex]n!=990k[/tex]

Now we know that:

[tex]990=2\times 3\times 3\times 5\times 11[/tex]

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

Since,

[tex]11!=1\times 2\times 3\times 4\times 5\times 6\times 7\times 8\times 9\times 10\times 11[/tex]

This means that :

[tex]n\geq 11[/tex]

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