Question

The LCM and HCF of the two numbers are 144 and 2 respectively. Find the least positive integer must be added to the product of two numbers so that it becomes a perfect square.

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

Answer 1

Correct Answer - Option 1 : 1

Given:

LCM = 144

HCF = 2

Formula\Concept used:

LCM × HCF = product of both numbers

Calculation:

⇒ Product of two numbers = 144 × 2 = 288

⇒ Now, nearest perfect square to 288 is 289 i.e 288 + 1

∴ 1 must be added to make 288 a perfect square.