Question

hcf and lcm of two numbers are 3 and 150 if the sum of the numbers is 81 what is the sum of reciprocal of the numbers ​

Answer 1

Answer :-

Given -

• HCF of two numbers = 3
• LCM of numbers = 150
• Sum of the numbers = 81

To Find -

• Sum of reciprocal

Solution :-

Let the numbers be x and y

We have to find -

➩ $\rm \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}$

We are given the sum of numbers, we have find the product of numbers -

➩ LCM × HCF = Product of two numbers

➩ x × y = 3 × 150

➩ xy = 450

Now we have,

• x + y = 81
• xy = 450

Substituting the values -

$\rm \frac{1}{x} + \frac{1}{y} = \frac{x + y}{xy}$

$\rm = \frac{450}{81}$

$\rm = 5.55$

➩ Sum of reciprocal of numbers = 5.55