Question

The HCF and LCM of two positive numbers are 1 and 90. If the greater number is three more than the three times of the smaller number. Find the greater number.
1. 8
2. 9
3. 18
4. 28

Answer 1

Correct Answer - Option 3 : 18

Given:

HCF of two numbers = 1

LCM of two numbers = 90

And, greater number is three more than the three times of the smaller number.

Formula used:

Product of two numbers = HCF × LCM

Calculation:

Let the smaller number be k

Then, the larger number = (3k + 3)

Now, Product of two numbers = HCF × LCM

⇒ k(3k + 3) = 1 × 90

⇒ 3k(k + 1) = 90

⇒ k² + k – 30 = 0

⇒ k² + 6k – 5k – 30 = 0

⇒ k(k + 6) – 5(k + 6) = 0

⇒ (k – 5)(k + 6) = 0

⇒ k = 5, -6

Greater number = (3k + 3)

⇒ 3(5) + 3

⇒ 18

∴ The greater number is 18.