Find the common element in two int arrays
Improving EnterArray1IntoHashSet

Why do you pass a hash set to EnterArray1IntoHashSet ?
It would be better to let the method create, populate and return the hash set.

You don't need to check if an element is inside a hash set before adding it:
if the element already exists, it will be simply ignored.

The name of this function is unnecessarily tedious.
It has a nice general purpose,
and you can name it accordingly.

static HashSet&lt;int&gt; ToHashSet(int[] array1)
{
    HashSet&lt;int&gt; set = new HashSet&lt;int&gt;();
    foreach (int num in array1)
    {
        set.Add(num);
    }
    return set;
}


Coding style

The placement of opening braces { is inconsistent:
sometimes you put it on the next line,
sometimes on the same line.
The .NET convention is to put it on the next line.

It's also unusual to put a space between method name and the ( when calling them, for example this:


Console.WriteLine (commonElement);



Just omit the unnecessary space:

Console.WriteLine(commonElement);