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Let m and n, (m<n), be two 2-digit numbers. Then the total number of pairs (m, n), such that (m, n)=6, is .
64
Let m=6a, n=6b with (a, b)=1 and a<b
10 6a and 6b 99 2 a<b 16
For each b, the number of a with 1 a<b and (a, b)=1 is (b)
b=216 (b)=1+2+2+4+2+6+4+6+4+10+4+12+6+8+8=79
These include a=1 with every b=2, 3, , 16: 15 pairs, which are not allowed (6a=6 is not a 2-digit number)
number of pairs =79-15=64
Answer: 64
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