Question

The LCM of 2 numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.

Answer 1

$\fbox\red{A}\fbox\green{n}\fbox\blue{s}\fbox\orange{w}\fbox\purple{e}\fbox\green{r}\downarrow$

Let the other number be 'x'

❥Given: LCM + HCF = 600

$\scriptsize\mapsto\mathsf{14 HCF + HCF = 600}$

$\scriptsize\mapsto\sf{15 HCF = 600}$

$\scriptsize\mapsto\sf{HCF = 400}$

$\scriptsize\mapsto\sf{LCM = 14 \times 40 = 60}$

$\scriptsize\mapsto\sf{Since \: HCF \times \: LCM=Product \: of \: 2 numbers}$

$\scriptsize\mapsto\sf{40 \times 560 = 280 \times x }$

$\footnotesize\mapsto\sf{x= \frac{40 \times 560}{280} }$

$\scriptsize\mapsto\sf{x=40 \times 2}$

$\scriptsize\mapsto\sf{x=80}$

✷Hence,The number is 80.