If HCF and LCM of two numbers are respectively

Question

If HCF and LCM of two numbers are respectively $(n - 1) a n d (n ² - 1) (n ² - 4)$ , then the product of the two numbers will be:

Smart Achievers · Accepted Answer

(3)

$W e h a v e, H C F = (n - 1) a n d L C M = (n ² - 1) (n ² - 4) W e k n o w t h a t p r o d u c t o f t w o n u m b e r s = L C M \times H C F S o p r o d u c t o f t w o n u m b e r s = (n - 1) (n ² - 1) (n ² - 4) = (n - 1) (n - 1) (n + 1) (n ² - 4) = (n + 1) (n - 1) ² (n ² - 4)$

Solution

Q.
If HCF and LCM of two numbers are respectively $(n - 1) a n d (n ² - 1) (n ² - 4)$ , then the product of the two numbers will be:

1 $(n ² - 1) (n ² - 4)$

2 $(n ² + 1) (n ² - 1) (n ² - 4)$

3 $(n ² - 4) (n + 1) (n - 1) ²$

4 $(n ² - 1) (n ² + 1) (n - 1)$

Ans.
(3)

$W e h a v e, H C F = (n - 1) a n d L C M = (n ² - 1) (n ² - 4) W e k n o w t h a t p r o d u c t o f t w o n u m b e r s = L C M \times H C F S o p r o d u c t o f t w o n u m b e r s = (n - 1) (n ² - 1) (n ² - 4) = (n - 1) (n - 1) (n + 1) (n ² - 4) = (n + 1) (n - 1) ² (n ² - 4)$

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Solution

Q. If HCF and LCM of two numbers are respectively (n – 1) and (n² – 1)(n² – 4), then the product of the two numbers will be:

1 (n² – 1)(n² – 4)

2 (n² + 1)(n² – 1)(n² – 4)

3 (n² – 4)(n + 1)(n – 1)²

4 (n² – 1)(n² + 1)(n – 1)

Ans. (3) We have, HCF = (n – 1) and LCM = (n² – 1)(n² – 4)We know that product of two numbers = LCM × HCFSo product of two numbers = (n – 1)(n² – 1)(n² – 4)= (n – 1)(n – 1)(n + 1)(n² – 4)= (n + 1)(n – 1)²(n² – 4)