Question

The LCM of two numbers is 156 and their HCF is 26. If the difference between the numbers is also 26, then the sum of the numbers is:
1. 52
2. 130
3. 78
4. 104

Answer 1

Correct Answer - Option 2 : 130

Given:

LCM of two number = 156

HCF of two number = 26

Difference between them = 26

Formula used:

LCM × HCF = first number × second number

Calculation:

Let the number be a and b respectively

According to question

⇒ a – b = 26

⇒ b = a - 26    ----(1)

LCM × HCF = a × b

⇒ 156 × 26 = a × (a - 26)

⇒ 4056 =  a² - 26a

⇒ a² - 26a – 4056 = 0

⇒ a² + 52a – 78a – 4056 = 0

⇒ (a + 52) (a – 78) = 0

⇒ a = 78 (a = -52 not possible as we need to take positive number)

⇒ b = a - 26 = 78 - 26 = 52

The sum of the number = (78 + 52)

⇒ 130

∴ Required sum is 130