Question

The sum of the H.C.F. and L.C.M. of two numbers is 680 and the L.C.M is 84 times the H.C.F. If one of the numbers is 56, then which of the following is the other number?

• A. 84
• B. 12
• C. 8
• D. 96
• E. 23

Answer 1

The correct option is D 96

Let x be the H.C.F. of two number 56 and k.
Let y be the L.C.M. of two numbers 56 and k.
To find k.
$\therefore xy=56k$
Also $x+y=680y=84x$ [Given]
$\Rightarrow 85x=680\Rightarrow x=8\Rightarrow y=673\Rightarrow 56k=8\times 672\Rightarrow k=96$
$\therefore$ the other number $=96$