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How many ordered pairs of positive integers (m,n) satisfy gcd(m,n) = 2 and lcm[m,n] = \(360\)?

 Feb 10, 2022
 #1
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1 = LCM of 90 and 8 = 360
GCD of 90 and 8 = 2
2 = LCM of 72 and 10 = 360
GCD of 72 and 10 = 2
3 = LCM of 40 and 18 = 360
GCD of 40 and 18 = 2
4 = LCM of 18 and 40 = 360
GCD of 18 and 40 = 2
5 = LCM of 10 and 72 = 360
GCD of 10 and 72 = 2
6 = LCM of 8 and 90 = 360
GCD of 8 and 90 = 2

 Feb 10, 2022
 #2
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REVISED LIST!

 

1 = LCM of 360 and 2 = 360
GCD of 360 and 2 = 2
2 = LCM of 90 and 8 = 360
GCD of 90 and 8 = 2
3 = LCM of 72 and 10 = 360
GCD of 72 and 10 = 2
4 = LCM of 40 and 18 = 360
GCD of 40 and 18 = 2
5 = LCM of 18 and 40 = 360
GCD of 18 and 40 = 2
6 = LCM of 10 and 72 = 360
GCD of 10 and 72 = 2
7 = LCM of 8 and 90 = 360
GCD of 8 and 90 = 2
8 = LCM of 2 and 360 = 360
GCD of 2 and 360 = 2

Guest Feb 10, 2022

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