eliminating unwanted records from carriage return / line feed combination in awk

Question

I am using GNU awk v4.2.0 from the Windows 7 x64 SP1 cmd.exe and ran into a problem with the following simple example:

# calculate the Greatest common divisor of each pair of inputs

BEGIN { RS="[\r\n]" }                                # added this

{
    arg1 =$1; arg2 = $2;

    if ((arg1 == "") || (arg2 == "")) { next }   # and added this

    while (arg1 != arg2)
    {
            if (arg1 > arg2)
                    arg1 -= arg2
            else
                    arg2 -= arg1
    }
    print "The greatest common divisor of", $1, "and", $2, "is", arg1
}

and a DOS formatted (CR/LF line endings) input file as follows:

75      30
24      60
360    224

the numbers are separated by spaces. The original awk script did NOT have the BEGIN statement setting RS, also it did NOT have the if statement that tests if arg1 or arg2 are empty. The original script would produce the following output:

 is 15eatest common divisor of 75 and 30
 is 12eatest common divisor of 24 and 60
 is 8reatest common divisor of 360 and 224

the results (15, 12 and 8) are in the wrong place because there is an unwanted carriage return in arg2.

To correct that problem, I added BEGIN { RS="[\r\n]" } which caused the output to be:

The greatest common divisor of 75 and 30 is 15
The greatest common divisor of  and  is
The greatest common divisor of 24 and 60 is 12
The greatest common divisor of  and  is
The greatest common divisor of 360 and 224 is 8
The greatest common divisor of  and  is

That made the value of the GCD appear at the end of the line where it's supposed to be but, it also caused unwanted/extraneous records to appear. To get rid of those I added the if ((arg1 == "") || (arg2 == "")) { next } which removed them.

Those steps caused the script to work as it should but, it seems to be a rather convoluted (not to mention undesirable) way of solving the problem.

my question is: is there a simpler, more natural, "awk like" way of making arg2 not include a carriage return in it ?