HCF of two numbers is 18.  If the sum of these two numbers and their LCM is 990.  How many pairs of such numbers are possible?

1

Let a, b are two coprime numbers, then

18a + 18b + 18ab = 990

a + b + ab = \(\frac{990}{18}\) = 55

add 1 both sides.

(1 + a) (1 + b) = 56

                       = 1 × 56 ..... (not possible)

                       = 2 × 28 ..... (i)

                       = 4 × 14 ..... (ii)

                       = 7 × 8 ..... (iii)

(i) and (ii), they all have common factor 2.

So, pairs (only 1)