Aptitude - Problems on H.C.F and L.C.M - Discussion

(a*b)product of number = l.c.m * h.c.f
2028 = x * 13
x = 156.
Which means
l.c.m = 156
h.c.f = 13

Now
156 = 2 x 6 x 13

Factorize the HCF

13 = 1 * 13

The HCF is the common factor for both numbers whereas the LCM contains all the unique factors of both numbers.

So, 13 is a common factor for both numbers.
The factors remaining are 2 and 6.

So, 2 is a factor of one number and 6 is the factor of the second number.

The first number = 13 x 2 = 26
The second number = 13 x 6 = 78

Hope it is clear now.

Now
Factorize the 26 and 78

26 = 2 * 13

78 = 6 * 13

Here 13 is the common value
So h.c.f. is 13 as given in question.
And
156 is the l.c.m.

And finally the number of pair is 1(13 only)

Then how answer as two(2).

Tell me clearly, how to solve, its my method is correct.

What is co-prime and why would we use it in this question?

Factors of:
6 = 1, 2, 3.
2 = 1, 2.

They have highest common factor 2. coprime are those pair that have 1 as hcf.

So only (1,12) and (4,3) are such pairs.

Hey 13a*13b=2028 then a*b=156 if we take 13 common and divide it by 2028.

Then how it is written that a*b=12?

Why we can not take pair as (1, 12), (4, 3), (3, 4), (12, 1)?

I think it should be 4 pairs.

(3, 4)4 = 1, 2, 4 why it is coprime number 2 number is also in the factor of 4.

There will be three pairs (26,78), (52,39), (156,13).

@Arvind, you must not consider (26, 78) because then the HCF will become 26; as given in the question HCF must be only 13.

Why are we considering coprimes?

We have to consider the co primes with 12.