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How many ordered pairs of positive integers (m, n) satisfy GCD(m, n) = 3 and LCM(m, n) = 108? Is there an alternative way than listing out ALL the possible combinations? If so, show your work.

 Oct 17, 2019
 #1
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LCM of 108 and 3 = 108
GCD of 108 and 3 = 3
LCM of 27 and 12 = 108
GCD of 27 and 12 = 3
LCM of 12 and 27 = 108
GCD of 12 and 27 = 3
LCM of 3 and 108 = 108
GCD of 3 and 108 = 3

 

 

Note: I do not know of  an "alternative way" other than listing them!!

 Oct 17, 2019

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