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 the other number is

• A. $60$4
• B. $50$
• C. $100$
• D. $80$

Answer 1

Answer: (D)

$80$

Let the other number be ${}^{\prime }{x}^{\prime }$

Given:$LCM+HCF=600$

$\Rightarrow 14HCF+HCF=600$

$\Rightarrow 15HCF=600$

$\Rightarrow HCF=40$

$\Rightarrow LCM=14\times 40=560$

Since HCFxLCM=Product of 2 numbers

=>$40\times 560$ = $280\times x$

$\Rightarrow x=\frac{40\times 560}{280}$

$\Rightarrow x=40\times 2$

$\Rightarrow x=80$

hence the other number is $80$.