Question

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. \(\dfrac{31}{480}\)

Answer 1

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 \(\frac{11}{160}\)