Question

LCM and HCF of two number are 120 and 5 respectively. How many such
pairs are possible?

Answer 1

Answer:-

HCF = 5 & LCM = 120


Solution is in this picture!!!

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Answer 2

Answer:

There  are 2  possible pair .

Step-by-step explanation:

Explanation :

Given ,  LCM of two number =  120

And HCF of two number = 5

LCM - The least common multiple of two figures is the “ lowest non-zero common number ” which is a multiple of both the figures.

HCF - Highest Common Factor is the topmost number which divides each of the two or further figures.

Step 1:

Let two number be a  and b .

Therefore , a = 5x and b = 5y      [where x and y are co - prime ]

As we know the property that is ,

Product of two given  numbers = product of LCM and HCF of that number

⇒ a× b = 120× 5

⇒5x × 5y = 600

⇒x y  =$\frac{600}{25}$= 24 = 1× 2× 2× 2× 3

And 24 can be written as ,

(1× 24 ), (2 × 12) , (4 × 6) , and (8 × 3)

⇒(1,24 ) ,(2 , 12 ) , (4 , 6) and (8,3)

Here , we can see that , (1 , 24 ) and (8 , 3) are co -prime

So we take only these two pair for x and y value

Therefore , x = 1 and 8

y = 24 and 3

But we have , a = 5x   and b = 5y

On putting the value of x and y we get ,

(5, 120 ) and (40 , 15 )

So these are the possible pairs.

Final answer :

Hence , 2 possible pair are  (5 , 120 ) and (40 , 15 ) .

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