Question

The HCF of two number is one sixth of the LCM of those number. I If one of the number is 15, Find the other?

Answer 1

Let us take the two numbers as h.x and h.y, where 'h' is the HCF.

Then the LCM would be h.x.y

From the question, h.x.y = 6 h (as HCF = 1/6 LCM and so LCM = 6 h)

Or, x.y = 6

There are two distributions of 6 over two numbers, 2*3 or 1*6

The numbers would then be 2h & 3h or h & 6h

Case I:

If one of the numbers is 15, the first case 2 h can't be 15, 3 h must be 15, 

thus the other number would be 2 h=10

Case II:

The second case 6 h can't be 15, h has to be 15, thus 6 h would be 90

thus, there are two possibilities for the 2nd number: 10 or 90

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Hence the number shall be 10 or 90

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