Question

The HCF and LCM of two numbers are $12$ and $72$, respectively. If the sum of the two numbers is $60$, then one of the numbers will be

• A. $12$
• B. $24$
• C. $60$
• D. $72$

Answer 1

The correct option is B $24$

Given, $HCF=12$, $LCM=72$

One number $=x$, Other number $=60-x$
$\therefore$ Product of the two numbers $=$ HCF $\times$ LCM
$\Rightarrow x(60-x)=12\times 72$
$\Rightarrow x^2-60x+864=0$
$\Rightarrow x^2-36x-24x+864=0$
$\Rightarrow x(x-36)-24(x-36)=0$
$\Rightarrow (x-36)(x-24)=0$

$\Rightarrow x=36$ or $24$
$\therefore$ One of the number is $24$.