When the greatest common divisor and least common multiple of two integers are multiplied, the product is 180.  How many different values could be the sum of the two integers?


[number theory](/questions/number-theory_138)
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  a       b

 180     1  
 90     2  
 60     3  
 45     4  
 36     5  
 30     6  
 20     9  
 18     10  
 15     12  
 12     15  
 10     18  
 9     20  
 6     30  
 5     36  
 4     45  
 3     60  
 2     90  
 1     180

  

 Just count them and sum them up, if that is what they want!

