Question

The difference of two numbers is $20$ and their product is $56.25$ times their difference. Find the LCM of the numbers

• A. $70$
• B. $1125$
• C. $225$
• D. $5$

Answer 1

The correct option is C $225$

Let the numbers be $a$ and $b$.

Then, $a - b = 20$ ........(i)
$ab=56.25\times 20=1125$
$\Rightarrow b=\frac{1125}{a}$
$\therefore$ Putting the value of b in (i) we get $a-\frac{1125}{a}=20$

$\Rightarrow a^2-1125=20a$
$\Rightarrow a^2-20a-1125=0$

$\Rightarrow a^2-45a+25a-1125=0$
$\Rightarrow a(a-45)+25(a-45)=0$

$\Rightarrow (a-45)(a+25)=0$

$\Rightarrow a=45$ or $-25$
Neglecting the negative value of $a$,

$\therefore b=45-20=25$
Now, $a=45=3^2\times 5,b=25=5^2$
$\therefore$ LCM of (45, 25) = $3^2\times 5^2=225$