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

128352/238368.

First, we take 128352
Then separate it into 3-digit.
Now find the diff btw 128 & 352 is 224.
224 is divisible by 7.
Follow the same way for 238368.

128 - 352 = 224(it is divisible by 7 and not divisible by 3,5,9)
238 - 368 = 130(it is divisible by 13 and not divisible by 4)
And then the answer is 7/13.

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.

@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, Just see the 1st 2 digits of the numerator and denominator it's 12 and 23, which is like their fraction is almost 1/2, so we can directly go for option verification.

>3/4 now way near to 1/2.
>5/13 will be much less than 1/2.
>9/13 is can't be 1/2.
>The only option left is 7/13 .

Instead of this go with the options;
1st check only the numerator divide with option A numerator.

Then check for B option with the numerator.
Then check for C option with the numerator.

128352/7 & 238368/13.
If divide you got your answer.
i.e C = 7/13.

First, find the HCF of the numerator and denominator which is 18336, then divide both the numerator and denominator by 18336. Therefore, the answer is 7/13.

Simple divisibility rule;

128352 is divisible by 7, 3
238368 is divisible by 13.

So, option is 7/13.

Let's break the fraction.

First, let's take the numerator:
128352=2⁵×3×7×191( prime factorization)--->1

And then now the denominator;

238368 = 2⁵ × 3 × 13 × 191--->2

From 1 and 2,
128352/238368 gives
2⁵ × 3 × 7 × 191/2⁵ × 3 × 13 × 191.

The answer is 7/13 since being all other terms (2⁵,3 and 191) cancelled.

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.

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