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How many ordered pairs of positive integers (m,n) satisfy gcd(m,n) = 22 and lcm(m,n) = 1100.

 Jan 29, 2021
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How many ordered pairs of positive integers (m,n) satisfy gcd(m,n) = 22 and lcm(m,n) = 1100.

 

[22 x 1100] = 24200 = 2^3 * 5^2 * 11^2 =[4 x 11] =44  and  11 x 25 x 2 ==550

Therefore:

m = 550  and  n= 44, or:

n = 44     and  m=550  

 Jan 29, 2021

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