Question

LCM of two numbers is $16$ times their HCF. The sum of LCM and HCF is $850.$ If one number is $50,$ then what is the number?

• A. $800$
• B. $1200$
• C. $1600$
• D. $2400$

Answer 1

Answer: (A)

$800$

Let the H.C.F be $x.$

Then L.C.M $=16x$ and another number is $n.$
Sum of the L.C.M and H.C.F,

$x+16x=850$

$\Rightarrow 17x=850$

$\Rightarrow x=50$
$L.C.M=\frac{productofthenumbers}{H.C.F}$
$16x=\frac{50\times n}{x}$

$16\times 50=\frac{50\times n}{50}$

$\therefore n=800$