LCM and HCF of two numbers are 90 and 15, respectively. If the sum of the two numbers is 75, then find the greater number.

45

LCM and HCF of two numbers are 90 and 15, respectively.

The sum of the two numbers is 75

 LCM × HCF = Product of two numbers

 Let one number be x

Other number = (75 - x)

 Then,

 ⇒ 90 × 15 = x(75 - x)

 ⇒ 1350 = 75x - x²

 ⇒ x² - 75x + 1350=0

 ⇒ x²- 45x - 30x + 1350=0

 ⇒ x = 45, 30

 ∴ Greater number = 45