## LCM & HCF

Hello all,
Can someone help me in solving this?
What is the number x?
(1) The HCF of x & 75 is 3
(2) The LCM of x & 75 is 225
Thanks in advance.

## Condition 1:The HCF of x &

**Condition 1:**
The HCF of x & 75 is 3
First what is HCF?
Highest Common Factor.
The number that is known is 75, if we factories we get
25 x 3 = 5 x 5 x 3
So, the possible values of x are 3, 6, 9, 12
(For 15 the HCF will be 5 and further the HCF will be higher)
**Condition 2:**
The LCM of x & 75 is 225
Now we ll chk this condition for all the numbers that we got from cond1 (i.e. 3 , 6, 9 , 12)
Number 3 satisfies condition 2nd that is LCM of 3 & 75 is 225
So the answer is x =3

## Dear Srikant you have given the wrong answer.

The answer is 9
As per condition 1 the x can be 3n ; n=1,2,3,4,5....
therefore x can be 3,6,9...
Now as per condition 2 The 75 has single power of 3 ,25 * 3
but 225 has 2 3's ie 25 * 3 *3
so x has to be 9 (3*3)
Thus the answer is 9
It cant be 3 else the LCM of 75 and x will come out to be 75 only not 225

## Yes you are rightSorry for

Yes you are right
Sorry for the mistake
And I think this is reason why so many of us get fewer percentiles than what we deserve
Silly mistakes

## Nothing Much tough

For ne two numbers m & n; it always holds:
HCF(m,n)X LCM(m,n)= m X n....
Solving we can easily get the other no. as 9.

## Guys,
On this forum i have

Guys,
On this forum i have seen lots of people trying to obtain answers by counting.Though this cannot be avoided at times i believe that solutions are possible the algebraic way for most of the problems. Counting takes a lot of time which we dont have the luxury of in CAT. just a thought :)

## True to some extentBut if

True to some extent
But if you are comfortable with numbers then it wonâ€™t take much time.
In the CAT latest trend with 2hr/30 mins and 75 questions, time is not a big constraint.
I personally find it very easy in solving questions with the very basic knowledge w/o remembering any tricks and short cuts.