Find all positive Integers

Question

Find all positive integers a and b such that 2m + 3d=78, when d is the greatest common divisor of a and b and m is the least common multiple of a and b

Answer 1

 

2m = 78 - 3d

 

m = (78 - 3d)/2  = 39 - 3d/2

 

d=2 --> m = 36 

 

d=4 --->  m = 33 <--  gcd must be odd or lcm must be even

 

d = 6 --> m = 30  --->  A  = 6 and b = 30

 

d = 8  ---> m = 27

 

d  = 10 ---> m = 24

 

d = 12 ---> m = 22

 

d = 14 --->m=20

 

d = 16 ---> m = 18

 

d = 18 ---> m  = 16 <--- can stop here

 

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