Question

The least common multiple of two numbers is 168 and highest
common factor of them is 12. If the difference between the numbers
is 60, what is the sum of the numbers?

Answer 1

Answer:

The and is 108

Step-by-step explanation:

Given∶

LCM of two numbers = 168

HCF of two numbers = 12

Difference of two numbers = 60

Calculation∶

Let two numbers be a and b be respectively.

Formula∶ Product of two numbers = Product of LCM and HCF of two numbers

⇒ a × b = 168 × 12

⇒ ab = 2016 ----(1)

a – b = 60 ----(2)

Formula∶ (a + b)2 – (a – b)2 = 4ab

Put the value of (1) and (2) into above expression,

⇒ (a + b)2 – (60)2 = 4 × 2016

⇒ (a + b)2 = 8064 + 3600 = 11664

⇒ a + b = 108.