Correct Answer - Option 1 : 2
Formula Used:
LCM × HCF = Product of numbers
Calculations:
Let the numbers be 7x and 7y.
LCM of 2 numbers = 105
HCF of 2 numbers = 7
LCM × HCF = Product of numbers
⇒ 105 × 7 = 7x × 7y
⇒ xy = 3 × 5 = 15
⇒ (x, y) = (3, 5), (5, 3)
⇒ (7x, 7y) = (21, 35), (35, 21)
⇒ Number of possible values of x and y = 2
∴ The number of possible values of x and y is 2.
The numbers are always multiples of hcf, so take 7x × 7y = 105 × 7 instead of x × y = 105 × 7.