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The LCM of the two numbers is 143 times their HCF. If both the numbers are 3 digit numbers and their HCF is 18, then what is the sum of the reciprocals of those two numbers?

The LCM of the two numbers is 143 times their HCF. If both the numbers are 3 digit numbers and their HCF is 18, then what is the sum of the reciprocals of those two numbers? Correct Answer <span class="math-tex">\(\dfrac{4}{429}\)</span>

Given:

LCM = 143 × HCF

Formual used: 

HCF × LCM = Product of the two numbers

Calculation:

Let, the two be number x and y

According to the question,

x × y = HCF × LCM

⇒ x × y = 143 × 18 × 18

⇒ x × y = 13 × 11 × 18 × 18

Since, 18 is HCF, so 18 will be present in both numbers

Then, x or y = 18 × 11

 x or y = 18 × 13

Now,

Sum of Recipropcal of numbers = 1/x + 1/y

⇒ (x + y)/xy

⇒ /(143 × 18 × 18)

⇒ (18 × 24)/(143 × 18 × 18) = 4/429

∴  The sum of the reciprocals of those two numbers is 4/429.

Hint

xy =  (143 × 18 × 18) and x + y = 

Where, 18 is common so,

(18 × 13 + 11) = 18 × 24

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