Question

The $LCM$ of two numbers is $14$ times their $HCF$. The sum of $LCM$ and $HCF$ is $600$. If one number is $280$, then find the second numbers.

• A. $80$
• B. $7$
• C. $140$
• D. $150$

Answer 1

The correct option is A $80$

Let the two numbers are $a$ and $b$

Let their HCF and LCM are $h$ and $l$ respectively.

$a=280$ is given.

Now $l$ is $14$ times the $h$

So,

$l=14h$ .............(1)

Sum of $l$ and $h$ is $600$

So,

$l+h=600$ ..........(2)

From (1) and (2),

$14h+h=600$

$15h=600$

$h=40$

From (1),

$l=14h$

$l=14\left(40\right)=560$

Relationship between HCF and LCM of two numbers $a$ and $b$ is,

$h\times l=a\times b$

$40\times 560=280\times b$

$\Rightarrow b=80$