Find the number of ordered pairs (a, b) such that a, b 10,11, , 29,30 and GCD (a, b)+ LCM (a, b)=a+b .

Step-by-step solution

aligned & g+l=a+b & g+ a b g =a+b & g^2+(a+b) g+a b=0 & (g-a)(g-b)=0 & g=a, b aligned For a=b , there will be 21 cases. If a=10, b may be 20 or 30 as well and vice-versa. . array ll a=11, & b=22 a=12, & b=24 a=13, & b=26 a=14, & b=28 a=15, & b=30 array ] 2=10 ways