Question

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

Answer 1

Answer:

Step-by-step explanation:

Correct option is

D

80

Let the other number be  

′

x  

′

 

Given:LCM+HCF=600

⇒14HCF+HCF=600

⇒15HCF=600

⇒HCF=40

⇒LCM=14×40=560

Since HCFxLCM=Product of 2 numbers

=>40×560 = 280×x

⇒x=  

280

40×560

​

 

⇒x=40×2

⇒x=80

hence the other number is 80.

Answer 2

$\bf\purple{QuestioN:-}$

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.

$\bf\blue{AnsweR:-}$

$\Large\sf\underline{Given:-}$

LCM of 2 numbers = 14 × their HCF

Sum of LCM & HCF = 600

One number = 280

$\Large\sf\underline{To\:Find:-}$

The other number = ??

$\Large\sf\underline{Solution:-}$

According to the given condition,

$\implies\bf{LCM=14\times\:HCF}$ ------------ Eq 1

$\implies\bf{LCM+HCF=600}$ ---------- Eq 2

On substituting Eq1 in Eq 2, we get,

$\implies\bf{14\:HCF+HCF=600}$

$\implies\bf{15\:HCF=600}$

$\implies\bf{HCF=\dfrac{600}{15}}$

$\implies\bf{HCF= 40}$ ----------- Eq 3

Now we got the value of HCF = 40.

On substituting Eq 3 in Eq2,

$\implies\bf{LCM+HCF=600}$

$\implies\bf{LCM+40=600}$

$\implies\bf{LCM=600-40}$

$\implies\bf{LCM=560}$

We know that,

Product of HCF & LCM = Product of that numbers.

ie,

$\implies\bf{LCM\times\:HCF=Product\:of\: the\: numbers}$

Let the unknown number be X.

Then,

$\implies\bf{560\times\:40=280\:\times\:X}$

$\implies\bf{22,400=280X}$

$\implies\bf{X=\dfrac{22400}{280}}$

$\implies\bf{X=80}$

•°• The Other Number, X = 80.

 

   

 

Happy Learning!!❤