Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 2)
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:
Answer: Option
Explanation:
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Discussion:
153 comments Page 14 of 16.
Dheeraj said:
1 decade ago
Let the two numbers be a,b.
HCF(a,b) is always a factor of LCM(a,b). The other two factors of LCM(a,b) are 13 and 14. Therefore the three factors of LCM(a,b) are 23, 13, 14.
LCM(a,b)=LCM(13,14,23)=13*14*23.
Now HCF(a,b)*LCM(a,b)=a*b
23*(23*13*14)=a*b, Therefore bigger number=23*14 and smaller number=23*13 (Since 23 is a common factor of both numbers).
HCF(a,b) is always a factor of LCM(a,b). The other two factors of LCM(a,b) are 13 and 14. Therefore the three factors of LCM(a,b) are 23, 13, 14.
LCM(a,b)=LCM(13,14,23)=13*14*23.
Now HCF(a,b)*LCM(a,b)=a*b
23*(23*13*14)=a*b, Therefore bigger number=23*14 and smaller number=23*13 (Since 23 is a common factor of both numbers).
Vinay said:
1 decade ago
Not convinced, please try to give some more practical sollutions, which is easy to understand.
Bharath k s said:
1 decade ago
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...
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...
Vivek said:
1 decade ago
I have an idea that HCF+LCM=a*b
Lalitha said:
1 decade ago
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 ?
(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 ?
Eshant said:
1 decade ago
I still didn't understnad the concept behind ths solution. Is their any easy method to solve these types of stuffs?
Hi_all said:
1 decade ago
@Chiya thanq :-*
Shakti said:
1 decade ago
@Chiya thanks for the solution.....
Neha said:
1 decade ago
@chiya. Why is 23 multiplied twice? Please explain?
Nitish said:
1 decade ago
Chiya has given the right answer.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers