Let m and n ,( m n ) be two 2-digit numbers. Then the total numbers of pairs (m, n) , such that gcd (m, n)=6 , is ________

Step-by-step solution

Let m =6 a , n =6 ~b m n a b where a & ~b are co-prime numbers also since m & n are 2 digit nos, so 10 m 99 & 10 n 99 i.e. 2 a 16 & 2 b 16 ( a is integer) Now 2 a b 16 & a & ~b are co-prime if a =2, ~b =3,5,7,9,11,13,15 a=3, b=4,5,7,8,10,11,13,14,16 a=4, b=5,7,9,11,13,15 a=5, b=6,7,8,9,11,12,13,14,16 a =6, ~b =7,11,13 a =7, ~b =8,9,10,11,12,13,15,16 a =8, ~b =9,11,13,15 a=9, b=10,11,13,14,16 a =10, ~b =11,13 a =11, ~b =12,13,14,15,16 a =12, ~b =13 a=13, b=14,15,16 a =14, ~b =15 a =15, ~b =16 64 ordered pairs