Answer:
There are 2 possible pair .
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 == 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 ) .