Question

The lcm of 2 positive real numbers is 105. If the hcf of these numbers is 7, then how many values of these numbers are possible?

1. 2
2. 3
3. 5
4. 4

Answer 1

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.