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?
LCM of 180 and 1 = 180
GCD of 180 and 1 = 1
LCM of 90 and 2 = 90
GCD of 90 and 2 = 2
LCM of 60 and 3 = 60
GCD of 60 and 3 = 3
LCM of 45 and 4 = 180
GCD of 45 and 4 = 1
LCM of 36 and 5 = 180
GCD of 36 and 5 = 1
LCM of 30 and 6 = 30
GCD of 30 and 6 = 6
LCM of 20 and 9 = 180
GCD of 20 and 9 = 1
LCM of 18 and 10 = 90
GCD of 18 and 10 = 2
LCM of 15 and 12 = 60
GCD of 15 and 12 = 3
