Question

the lcm and hcf of 2 non - zero positive number are equal, then the number must be​

Answer 1

Answer:

HCF being the highest common factor is always a factor of both the numbers. Therefore the numbers can be written as multiples of HCF. ⇒a=1,b=1 ( since a and b are natural numbers). Therefore, the two numbers are the equal.

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Answer 2

SOLUTION

TO DETERMINE

The LCM and HCF of 2 non - zero positive number are equal, then the number must be

CONCEPT TO BE IMPLEMENTED

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

EVALUATION

Let a and b are two non - zero positive number

Such that LCM = HCF = k

Then we have

a = mk and b = nk

We know that

HCF × LCM = Product of the numbers

$\displaystyle \sf{ \implies k \times k = a \: \times b}$

$\displaystyle \sf{ \implies k \times k = mk \: \times nk}$

$\displaystyle \sf{ \implies mn {k}^{2} = {k}^{2} }$

$\displaystyle \sf{ \implies mn = 1}$

Since m and n are non - zero positive number

Then m = 1 , n = 1

So we have a = k , b = k

Which gives a = b

Thus the two number must be equal

FINAL ANSWER

The LCM and HCF of 2 non - zero positive number are equal, then the number must be equal

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