Question

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

• A. 22
• B. 24
• C. 26
• D. 28

Answer 1

The correct option is C 26

$\text{Let the first number}=x$
$\text{Then, second number}=x+2$
$HCF=2$
$LCM=84$
We know that the product of two numbers $=HCF\times LCM$
$\Rightarrow x\times (x+2)=2\times 84$
$\Rightarrow x²+2x-168=0$
$\Rightarrow x²-12x+14x-168=0$
$\Rightarrow x(x-12)+14(x-2)=0$
$\Rightarrow x=12,x+2=14(\because \text{Both the numbers are positive.)}$
$\Rightarrow x+x+2=12+14=26$