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?
Answer & explanation
Correct answer: option 3
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)