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The L.C.M and H.C.F of two numbers is 585 and 13 respectively. Find the difference between the numbers.


1. 39
2. 52
3. 67
4. 71

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Correct Answer - Option 2 : 52

Given:

H.C.F of numbers = 13

LCM of numbers = 585

Calculation:

 Let the number be 13a and 13b where a and b are co-prime.

L.C.M of 13a and 13b = 13ab

According to question, 13ab = 585

⇒ ab = 45

⇒ ab = 5 × 9

⇒ a = 5 and b = 9 or a = 9 and b = 5

⇒ First number = 13a

⇒ First number = 13 × 5

⇒ First number = 65

⇒ Second number = 13b

⇒ Second number =13 × 9

⇒ Second number = 117

Required difference = 117 - 65 = 52

∴ Required difference = 52

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