Let us x = h * a; y = h * b

a and b are co-prime. So, LCM of (x, y) = h * a * b

So, in essence h + h * a * b = 91. Or h(ab + 1) = 91

Now, 91 can be written as 1 * 91 or 7 * 13

Or, we can have HCF as 1, LCM as 90 -

There are 4 pairs of numbers like this (2, 45), (9, 10), (1, 90) and (5, 18)

We can have HCF as 7, ab + 1 = 13 => ab = 12 => 1 * 12 or 4 * 3

Or, the pairs of numbers are (7, 84) or (21, 28)

The third option is when HCF = 13, ab + 1 = 7 => ab = 6

Or (a, b) can be either (1, 6) or (2, 3)

The pairs possible are (13, 78) and (26, 39)

There are totally 8 options possible - (2, 45), (9, 10), (1, 90), (5, 18), (7, 84), (21, 28), (13, 78) and (26, 39).

8 Pairs.

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