Question

The sum of two numbers is 220. The LCM and HCF of the two numbers are 264 and 44 respectively. Find the difference of the two numbers.​

Answer 1

Answer:

44

Step-by-step explanation:

Let the two numbers be x and y

Sum of two numbers = 220

⇒ x + y = 220

LCM of two numbers = 264

HCF of two numbers = 44

We know that

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

⇒ xy = 264 × 44

⇒ xy = 11616

We know that

(x - y)² = (x + y)² - 4xy

⇒ (x - y)² = 220² - 4( 11616 )

⇒ (x - y)² = 48400 - 46464

⇒ (x - y)² = 1936

⇒ x - y = √1936 = 44

Difference of the two numbers = 44