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
