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

In the options, mostly the denominator is 13.

If we divide 238368 by 13, we can get the exact number which divides both 128352 and 238368.
238368/13=18336 whose last digit is 6.
In 128352 the last digit is 2.
If multiply 6 by 7, then we can get the last digit as 2.
So, the answer is 7/13.

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

Anyone, please explain me in detail to understand the answer.

@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.

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.

@All.

We can Find the unit place by cross-multiplying.

@Punni.

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

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**

The formula is;

Product of LCM & HCF = product of two numbers.

Guys, I have an idea over here for quick solution of this problem at first, 128352/238368 = 0.53 find this fraction value by dividing the stuff given in the question and then from all the options of answer divide each of them and find the fraction like 3/4 = 0.75 and so on for other four and finally when the decimal value matches with the above found value it is the answer i.e is 7/13 = 0.53, that's it.