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

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.28)

28. 

The L.C.M. of two numbers is 48. The numbers are in the ratio 2 : 3. Then sum of the number is:

[A]. 28
[B]. 32
[C]. 40
[D]. 64

Answer: Option C

Explanation:

Let the numbers be 2x and 3x.

Then, their L.C.M. = 6x.

So, 6x = 48 or x = 8.

The numbers are 16 and 24.

Hence, required sum = (16 + 24) = 40.


Mythili said: (Jun 30, 2010)  
How 6x came? please explain.

Uma Upadhyay said: (Oct 14, 2010)  
@ Mythlili

The LCM of 2 &3 is 6 taking X as common factor, the LCM of 2x & 3x will 6X.

Uttam said: (Feb 3, 2011)  
Product of two numbers = Product of their H.C.F. and L.C.M.
consider HCF as X,
so,
two nos are 2X and 3X
then,
2X*3X=X*48.
solving for X
X=48/6
we get
X=8
so the nos,16,24
and ans 40.

Ritu said: (Jun 17, 2011)  
How came 16 and 24 ?

Gufran said: (Sep 29, 2011)  
Already uttam find....X=8.
and we have 2X&3X=2*8=16 & 3*8=24

Arif said: (Apr 2, 2012)  
Here you do 2x and 3x. The sum of two. So 2x*3x=6x2. Why 6x?

Ambi said: (Apr 2, 2012)  
Why its not X square? and only X. While solving mathematically it should be x square?

Roma said: (Jun 6, 2014)  
It's so simple.

Let h.c.f means multiply and l.c.m means divide.

So 2/48 = 1/24.
And 3/48 = 1/16.

Let take additon of 16+24 = 40.

Sanjay Kiran said: (Nov 12, 2014)  
How 16 and 24 got? Please explain.

V!Cky said: (Sep 5, 2015)  
Product of two number = Product of HCF and LCM.

Here we go to solve problem:

48 = x*{3*2}.
48/6 = x.
x = 8.

3x:2x = 3*8:2*8.

1st number 24:2nd number 16.

= 40.

Rakesh.H said: (Aug 17, 2016)  
Simple way.

48/2 = 24.
48/3 = 16.
24 + 16 = 40.

Prem said: (Oct 10, 2017)  
Very simple way, 2:3 means sum is always a multiple of 5. Here only multiple of 5 is 40.

Tanmay Punse said: (Jun 29, 2018)  
@Ambi.

It's so simple,
Then x of HCF and x in 6x^2 gets cancelled.
And hence 6x is remained.

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