Question

There are wallpapers of two different sizes, $6{\text{feet}}^2$ and $8{\text{feet}}^2.$ What should be the minimum area of the wall, which can be fully covered using some identical wallpapers of any of given type?

• A. $24{\text{feet}}^2$
• B. $12{\text{feet}}^2$
• C. $6{\text{feet}}^2$
• D. $48{\text{feet}}^2$

Answer 1

The correct option is A $24{\text{feet}}^2$

As any of the two wall papers can be used, the wall area should be a multiple of area of both the wallpapers.

The minimum area of wall which can be fully covered using any of these two wallpapers is the LCM of $6{\text{feet}}^2$ and $8{\text{feet}}^2.$

Prime factorisation of both the area is as follows:
$6=2\times 3$
$8=2\times 2\times 2$

LCM of $6$ and $8$ is $=2\times 2\times 2\times 3=24$.

$\therefore$ Required area is $24{\text{feet}}^2.$