Question

The product and HCF of two numbers are 2160
and 12 respectively. Accordingly, find the num-
ber of such pairs possbile ?

Answer 1

Answer:

calculation in mathematics say,

Product of two numbers is equal to the product of their HCF and LCM.

So if we take two numbers as a and b we have,

a x b= HCF(a,b) x LCM(a,b)

Thus,

2160 = 12 x LCM(a,b)

LCM(a,b) = 180

The question says, HCF is 12. This means both the numbers have 12 as a common factor which means the numbers can be

a = 12 x r …1

b = 12 x s …2

Where r and s are the numbers to which 12 is multiplied to get the original number. As per the question,

a x b = 2160

As per 1 and 2

12 x r x 12 x s = 2160

r x s = 15 …3Now only 2 values are possible for r and s for 3 to be true,

r = 3, s = 5 or s = 3, r = 5

Let us take, r = 3, s = 5,

So, a = 12 x 3 = 36 b = 12 x 5 = 60

Now, 36 x 60 = 2160

HCF(36,60) = 12

LCM(36,60) = 180

So, the two numbers are 36 and 60 respectively.

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Answer 2

Step-by-step explanation:

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