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

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**

@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.

@All.

Simply it can be solved by;

Goto the Option wise and use divisibility Rule.

1) Option "C" is Correct

Rule of Divisible 7 :- The difference the two alternate group take in 3 digits at a time should either be 0 or 7

Rule of 13 : difference between Alternate group 3digit which is Divisible 13..


As per rule 128352:-
352 224/7 = Reminder is 0
- 128
-----------
224

Therefore 7 is divisible by NUMERATOR.

(238268):-
368 130/13
- 238 (13 is divisible by NUMERATOR)
----------
130
Therefore 13 is Divisible by DENOMINATOR.

So, options C is the Right Answer.

@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.

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.

Simple check option A.

3*1 = 3....128352 not match the last number i.e. 3&2.
3*2 = 6....128352 not match the last number i.e. 3&2.
...
3*4 = 12...128352 now match the last number i.e. 2&2.

Now 4*4 = 16...238368 not match the last number i.e. 6&8.

Check option C.

7*6 = 42....128352 now match the last number i.e. 2&2.

Now 13*6 = 78...238368 now match the last number i.e. 8&8.

I hope it can help,

Let's apply divisibility rule:

Divisibility by 5: Last digit 0 or 5.

Divisibility by 9: Sum of digits = 9 or multiple of 9.

So, as per given numerators of options B and D, these conditions are not satisfied. Hence neither B nor D is answer.

Divisibility by 4: Last two digits 0 or multiple of 4 not being satisfied in option A's denominator. Hence correct option is C.

Just find the H.C.F. of 128352 & 238368.(Using Division method).

The HCF is 18336.
Now see the last digit of the numerator i.e., '2'. And last digit of HCF is '6'.
If 6*X=_2 i.e., either 6*2=12, or 6*7=42.
So, the numerator is either 2 or 7.
In the given options there is no number with numerator 2, But there is a number with numerator 7. i.e., option (C) 7/13.

238368-128352 = 110016.

128352-110016 = 18336.

110016-18336 = 91680.

18336-91680 = (negative, so not taken).

If we do 238362/91680 = 2.6(in decimal, so not taken).

And 128352/91680 =1.4 this too.

So now, take 128352/18336 = 7 and 238368/18336 = 13.

Two are integers, not in decimals.

So we take this value friends.

Now answer is 7/13.

It can be solved even more efficiently.

Since we have 13 in denominator among options.

238368/13 = 18336.

Now Cross check options to know unit place value.

18336*7=_______2.

18336*5=_______0.

18336*9=_______9.

And the numerator has 2 In units place so go with option 7/13.

This always works if we don't have non of the above as option.