Question

The L.C.M. of two numbers is $(a+b)$ and their H.C.F. is $k(a-b)$. If one of the numbers is k, find the other number

• A. $\frac{ka}{b}$
• B. $a^2-b^2$
• C. $\frac{a+b}{k(a-b)}$
• D. $\frac{ka+b}{ka-b}$

Answer 1

Answer: (B)

$a^2-b^2$

given that for two numbers

$HCF=k(a-b)$

$LCM=a+b$

one number is $k$

using the formula

$HCF\times LCM=n\times m$

where $n,m$ are two numbers

Now

$k(a-b)\times (a+b)=k\times m$

$(a-b)\times (a+b)=m$

$\Rightarrow m=a^2-b^2$

The other number is $a^2-b^2$