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

@ : Home > Aptitude > Problems on H.C.F and L.C.M > General Questions - Discussion

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"Forgiveness is a virtue of the brave."
- Indira Gandhi
2. 

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

[A]. 276[B]. 299
[C]. 322[D]. 345

Answer: Option A

Explanation:

Clearly, the numbers are (23 x 13) and (23 x 14).

Larger number = (23 x 14) = 322.


Abhinav said: (Sat, Sep 25, 2010 10:53:12 AM)    
 
What is the concept behind this solution?

Sinchana said: (Fri, Dec 31, 2010 11:47:56 PM)    
 
I didn't understand the solution can anybody explain for me.

Archana said: (Sat, Jan 1, 2011 12:06:40 AM)    
 
Could not understand the concept, please help.

Poornima said: (Thu, Jan 27, 2011 07:26:12 PM)    
 
HCF- Higest Common Factor, so we already have one factor of the number we need to find out ok. N we are also given the least common factors ie, 13 n 14. So to get the numbers just multiply both the Least common numbers with their HCF so that you can find the actual numbers.

Riya said: (Sun, Feb 27, 2011 11:29:16 AM)    
 
Not convinced.

Prathyusha said: (Sun, Mar 6, 2011 12:51:02 PM)    
 
1]HCF of two numbers is the number which is common factor for both numbers given.here 23 is the common factor.

2]other than this common factor ,we also will have the product of uncommon factors for the two numbers (13 and 14 here).

3]the first number =23*13
and second number=23*14

4]greatest of two numbers is definitely 23*14

Correct me if i am wrong please!.....

Pramod said: (Tue, Mar 15, 2011 03:14:03 AM)    
 
Now what are these uncommon factors?

Chiya said: (Fri, Apr 22, 2011 02:18:39 AM)    
 
HCF*LCM=a*b
23*(13*14)=a*b
(23*13)*(23*14)=a*b
a=23*13
b=23*14

Therefore b = 23*14 is the greatest.

Ramesh said: (Sat, Apr 30, 2011 11:33:54 PM)    
 
I think the two numbers can be 23 and 23x13x14 i e 4186. Is it possible?
Suppose we take two numbers 4 and 24. Their HCF is 4 and LCM is 24. Then the greatest number is 24 itself even though it is the LCM.Am I right?

Avinash said: (Mon, May 9, 2011 10:35:56 AM)    
 
What pratyusha said is h.c.f of two numbers that means common factor of two numbers is 23.

Hope there are more than common factors..
then what about uncommon factors..they given lcm of two factors..is uncommon factors are lcm of factors?

I want clear explanation

Anoop said: (Sat, Jun 11, 2011 09:15:43 AM)    
 
Let first number = 23 *a and second number = 23 * b where a and b are the products of the uncommon factors and they will be different numbers.

lcm=23*13*14
that means 23*a*__=23*b*__ = 23 * 13 * 14
a*__ = 13*14
b*__ = 13*14
a and b are two different numbers
so either a=14 & b=13
or a=13 and b = 14

so the numbers are 23*13 and 23 *14

Parvez said: (Sat, Jul 2, 2011 06:30:09 AM)    
 
Ya I understand but I'm not fully satisfied to this method.

Please give me suggestion.

#@Dev# said: (Sat, Aug 6, 2011 05:40:37 PM)    
 
13 and 14 are two factors doesn't mean that 13 belongs to one no. and 14 belongs to another one

It may be like 26 belongs to greater no and 7 belongs to lower one.

Nitish said: (Sun, Sep 4, 2011 04:11:17 PM)    
 
Chiya has given the right answer.

Neha said: (Thu, Sep 15, 2011 03:02:33 PM)    
 
@chiya. Why is 23 multiplied twice? Please explain?

Shakti said: (Sun, Sep 25, 2011 03:27:26 PM)    
 
@Chiya thanks for the solution.....

Hi_All said: (Tue, Oct 25, 2011 08:52:58 PM)    
 
@Chiya thanq :-*

Eshant said: (Fri, Nov 11, 2011 09:39:01 PM)    
 
I still didn't understnad the concept behind ths solution. Is their any easy method to solve these types of stuffs?

Lalitha said: (Wed, Dec 21, 2011 01:33:14 PM)    
 
What chiya said is totally wrong
(H.C.F)*(L.C.M)=a*b this is right but
Chiya said: (Fri, Apr 22, 2011 02:18:39 AM)

HCF*LCM=a*b
23*(13*14)=a*b
(23*13)*(23*14)=a*b
a=23*13
b=23*14

Therefore b = 23*14 is the greatest.

23*(13*14)=a*b
(23*13)*(23*14)=a*b This is wrong.

Answer is right but logic is wrong. Anybody explain it clearly ?

Vivek said: (Fri, Feb 10, 2012 10:48:47 PM)    
 
I have an idea that HCF+LCM=a*b

Bharath K S said: (Sun, Feb 12, 2012 02:51:13 PM)    
 
They have given hcm of two numbers which is same for both the numbers..
hcm=23,23.
lcm of the two numbers are 13 and 14
lcm=13,14.
from this we should find the two unknown numbers x&y.
x=(lcm of x)*(hcm of x) therefore x=13*23=299.
y=(lcm of y)*(hcm of y) therefore y=14*23=322.
now we hav found the two unknown numbers and the biggest of them is 322, which is the ans...

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