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

Please explain with easy method.

Go with options.

Check whether numerator and denominator both are divisible by values given in option.

Here only 3/4 and 7/13 satisfy the condition.

Now apply logic to get the answer (here denominator (238368) is approx. Double of numerator(128352) Hence 7/12 is answer as denominator (13) is approx. Double of numerator(7).

128352/238368 is simplified to 12/23 (i.e first to digits from numerator and denominator)
It will give approximately 0.48.

Now check in options which one is nearer to 0.48.

7/13 is the answer.

Hope it helps.

@Yuvaraj .

12/23 is 0.52 it's not 0.48.

7*6=42.
13*6=78.

Just see unit digit number it's 2 and 8 respectively so my answer is 7/13 only.

@Sanket Shinde.

Why you multiply 7 &6? Explain.

Can anyone explain the solution in another method to get it easily?

@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.

How to get 18336? Please explain.

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**