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

(2*2*2*2*2*3*7*191)/(2*2*2*2*2*3*2483)
Gives;
(7*191)/(2483) = 7/13.

@All.


These are our factors. write them as ascending order we found.
5/13, 7/13, 9/13 and 3/4.

Now we divide the given number's numerator and denominator by (5/13, 7/13, 9/13 and 3/4) these numbers' numerator and denominator. (such as given number's numerator/one of those option's numerator)

First, 5/13.

128352/5= not divisible (so the first option is out, no need to check the denominator)

Second,
7/13

128352/7 = 18,336
238368 /13 = 18, 336

So here is the answer 7/13. Because the least number is not able to divide the given number. latter is divisible by 7/13. And the next numbers are greater than 7/13.

I think option A is also divisible and also lowest. So why can't it be opton A?

Take 128352.

Let's divide into two parts 128 352.
subtract 352-128= 224,
as we know 224 is divisible by 7( taking numerator from options),
We confirm the numerator is 7.

Same for denominator 238 368.
368-238 = 130,
130 divisible by 13,

So, 7/13 is the answer.

Reduce the no to 12/23.
it is approx 1/2.

So, find an option that is close to 1/2(i.e) 7/13.

@Punni.

How can we take out factors of such a big number? Explain, please.

Thanks @Sona.

Thanks for giving an easy solution @Vaishak.

@All.

According to me, the solution is;

1. We simply take out the factors by just orally dividing...which i hope we can all do it at this level.

2. So 128352 = 2 x 64176.
= 2 x 2 x 32088,
= 4 x 4 x 8022,
= 16 x 2 x 4011,
= 32 x 3 x 1337,
= 32 x 3 x 7 x 191.

3. Similarly, 238368 = 4 x 59592.
= 4 x 4 x 14898,
= 16 x 2 x 7449,
= 32 x 3 x 1337,
= 32 x 3 x 13 x 191.

4. Now when we put this in form, 32 x 3 x 7 x 191/ 32 x 3 x 13 x 191 = 7/13.

Hope, this helps you all to understand.

For suppose let us assume their hcf be X.
Then ( X*u)/(X*v)= 128352/238368.

Where u,v are the co primes

Eg: here in case of option A : u =3 and v= 4 similarly for remaining options also..!!
Here the question gets easily solved if we verify the options as follows........

--Firstly if u observe both the options i.e A and C are satisfying the numerator and denominator.

i.e 128352 is divisible by both 3 and 7
238368 is divisible by both 4 and 13

Since both the options are satisfying we need to go for another option elimination process which will be b/w option A and C

---here if u observe clearly for option A the last digit of X in case of X*u is not satisfied by the last digit of X in case of X*...but it is not the case with option C as the last digits of both X's in case X*u and X*v are same .......

Which implies option C is the correct answer.

Note:-

**The above process won't even take more than 5min and this process reduces the complexity of solving as it won't involve finding the exact HCF value**