Question

1. The LCM of two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find the
HCF of two numbers.
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Answer 1

Answer:

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Answer 2

Answer :

›»› The HCF of two required numbers is 50 and 450 respectively.

Step-by-step explanation :

Given :

• The LCM of two numbers is 9 times their HCF.
• The sum of LCM and HCF is 500.

To Find :

• The HCF of two required numbers.

Solution :

Let us assume that, the LCM is "x" and HCF is "y" respectively.

As it is given that, LCM of two numbers is 9 times their HCF.

→ x = 9y ................(1)

As it is also given that, the sum of LCM and HCF is 500.

→ x + y = 500 .............(2)

Our equations are,

• x = 9y ................(1)
• x + y = 500 .............(2)

Substituting the value of x in equation (2), we get :

→ 9y + y = 500

→ 10y = 500

→ y = 500/10

→ y = 50/1

→ y = 50

Substituting the value of y in equation (1), we get :

→ x = 9(50)

→ x = 450

Hence, the HCF of two required numbers is 50 and 450 respectively.