# The HCF and LCM of two numbers is 15 and 480 respectively. What is sum of their reciprocals ?

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The HCF and LCM of two numbers is 15 and 480 respectively. What is sum of their reciprocals ?
1. $\dfrac{11}{160}$
2. $\dfrac{1}{32}$
3. $\dfrac{1}{15}$
4. $\dfrac{31}{480}$

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Correct Answer - Option 1 : $\dfrac{11}{160}$

Given:

HCF = 15

LCM = 480

Formula used:

HCF × LCM = a × b

Calculation:

Let the number be 15a and 15b

15a × 15b = 15 × 480

⇒ ab = 7200/225

⇒ ab = 32

Now we will check for co-prime factors for the 32

(1, 32) (2, 16) and (4, 8)

There is only one pair (1, 32) which is co-prime

So the number will be

15a = 15 × 1 = 15

15b = 15 × 32 = 480

Sum of their reciprocal

$\dfrac{1}{15} \ + \ \dfrac{1}{480} = \dfrac{32 \ + \ 1 }{480}$

$\dfrac{33}{480} = \dfrac{11}{160}$

∴ The sum of their reciprocal is $\frac{11}{160}$