If the HCF and LCM of two consecutive (positive) even numbers is 2 and 84, the sum of the numbers is:

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Solution

The correct option is C 26
$Let the first number$
$Then, second number = x + 2$
$H C F = 2$
$L C M = 84$
We know that the product of two numbers $= H C F \times L C M$
$\Rightarrow x \times (x + 2) = 2 \times 84$
$\Rightarrow x 2 + 2 x - 168 = 0$
$\Rightarrow x 2 - 12 x + 14 x - 168 = 0$
$\Rightarrow x (x - 12) + 14 (x - 2) = 0$
$\Rightarrow x = 12, x + 2 = 14 (∵ Both the numbers are positive.)$
$\Rightarrow x + x + 2 = 12 + 14 = 26$

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Similar questions

Question 26
Which of the following statements is not true?

(A) The HCF of two distinct prime numbers is 1
(B) The HCF of two co-prime numbers is 1
(C) The HCF of two consecutive even numbers is 2
(D) The HCF of an even and an odd number is even.

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If the HCF and LCM of two consecutive (positive) even numbers is 2 and 84, the sum of the numbers is: [1 mark]

The correct option is C 26Let the first number Then, second number =x+2 HCF=2 LCM=84 We know that the product of two numbers =HCF×LCM ⇒x×(x+2)=2×84 ⇒x2+2x−168=0 ⇒x2−12x+14x−168=0 ⇒x(x−12)+14(x−2)=0 ⇒x=12,x+2=14(∵ Both the numbers are positive.) ⇒x+x+2=12+14=26

If the HCF and LCM of two consecutive (positive) even numbers is 2 and 84, the sum of the numbers is:

[1 mark]