# 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

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.