Question

If hcf and lcm of two positive even numbers are 2 and 84 respectively what will their sum

Answer 1

Answer:

The numbers are 12 and 14

The sum of the numbers is 12+14=26

Step-by-step explanation:

Given that hcf and lcm of two positive even numbers are 2 and 84 respectively

That is  HCF = 2 and LCM = 84

Let the two consecutive even numbers be 2x and 2(x + 1)

LCM of 2x and 2(x + 1)=2x(x + 1)

Which implies that 2x(x + 1)=84

$x(x + 1)\frac{84}{2}$

$x(x+1)=42$

$x^2+x=42$

$x^2+x-42=0$

$(x+6)(x-7)=0$

x+6=0 or x-7=0

x=-6 or x=7

We have to take positive value only

Therefore x=6

Since the numbers are 2x and 2(x+1) substitute x=6 we get

2(6)=12 and 2(6+1)=2(7)=14

Therefore the numbers are 12 and 14

The sum of the numbers is 12+14=26