Question

if HCF (x,14)=6,LCM(x,14)=28 then find the value of x​

Answer 1

SOLUTION

CHANGE IN QUESTION

Here HCF ( x , 14 ) = 6 is not valid

Since 6 is not a factor of 14

We take the question as below :

If HCF ( x , 14 ) = 2 and LCM ( x , 14 ) = 28 then find the value of x

GIVEN

• HCF ( x , 14 ) = 2

• LCM ( x , 14 ) = 28

TO DETERMINE

The value of x

FORMULA TO BE IMPLEMENTED

We are aware of the relationship between HCF and LCM of two numbers that

If for two numbers HCF and LCM are given then

HCF × LCM = Product of the numbers

EVALUATION

Here the given two numbers are x and 14

Now it is given that

HCF ( x , 14 ) = 2 and LCM ( x , 14 ) = 28

∴ HCF × LCM = Product of the numbers

$\sf{x \: \times 14 = 2 \times 28}$

$\displaystyle \sf{ \implies \: x = \frac{2 \times 28}{14} }$

$\implies \sf{x = 4}$

FINAL ANSWER

The required value of x = 4

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Answer 2

Given: HCF (x,14) = 6,LCM (x,14) = 28

Mistake in the given question  

As we know that HCF is always a factor of LCM but in this question 6 is not the factor of  28.

Correct question:

If HCF ( x , 14 ) = 2 and LCM ( x , 14 ) = 28 then find the value of x

To Find : Value of x

Solution:

LCM of two numbers = 28  , HCF of two numbers = 6 and second number = 14

We know that,

LCM x HCF = first number x second number

28 x 2  = x ×  14

First number = ( 28 x 2 ) /14  

First number = 56/14  

First number = 4  

Hence, the value of x is 4.

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