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 8 of 16.
Yunus said:
1 decade ago
If the two Nos are A and B.
LCM factor of A=13 and that of B=14 (by doing LCM).
And HCF of A and B is 23.
Than the No is always HCF*A =23*13 / HCF*B=23 *14.
Hence B=322 is larger No.
LCM factor of A=13 and that of B=14 (by doing LCM).
And HCF of A and B is 23.
Than the No is always HCF*A =23*13 / HCF*B=23 *14.
Hence B=322 is larger No.
Erica Ferrao said:
9 years ago
a * b = lcm * (hfc)^2.
a * b = lcm * hfc * hfc.
a * b = (14 * 13) * 23 * 23,
a * b = (14 * 23) * (13 * 23),
a = 14*23 and b = 13 * 23,
a > b,
=>a = 322.
Correct me if I am wrong.
a * b = lcm * hfc * hfc.
a * b = (14 * 13) * 23 * 23,
a * b = (14 * 23) * (13 * 23),
a = 14*23 and b = 13 * 23,
a > b,
=>a = 322.
Correct me if I am wrong.
SUMI said:
1 decade ago
@poornima.
Well explained.
hcf*lcm = n1*n2 = N1(let n1*n2=N1 for lcm=13).
Case1:
23*13=N1;
similarly,
Case2:
23*14=N2;(n1*n2=N2 for lcm=14).
So N2>N1.
Well explained.
hcf*lcm = n1*n2 = N1(let n1*n2=N1 for lcm=13).
Case1:
23*13=N1;
similarly,
Case2:
23*14=N2;(n1*n2=N2 for lcm=14).
So N2>N1.
#@Dev# said:
1 decade ago
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.
It may be like 26 belongs to greater no and 7 belongs to lower one.
Monalisha said:
7 years ago
let two numbers be 23x and 23y then
LCM=23xy.
Since other two factors are 13 and 14
LCM=23x13x14.
hence, the two no. are 23x13 and 23 x 14,
larger is =23 x 14=322.
LCM=23xy.
Since other two factors are 13 and 14
LCM=23x13x14.
hence, the two no. are 23x13 and 23 x 14,
larger is =23 x 14=322.
Abhi said:
8 years ago
In question factors of LCM is 23, 13, 14 (read question).
&in the both number 23 factor required for make HCF 23 so least number is 23*13& greater 23*14.
&in the both number 23 factor required for make HCF 23 so least number is 23*13& greater 23*14.
Smitten Ediot said:
9 years ago
As per the given information of the question,
We know HCM is 23 and LCM is 23 * 13*14.
Hence No 1 = 23 * 13, No2 = 23 *14.
Hence, 23*14 is the largest Number.
We know HCM is 23 and LCM is 23 * 13*14.
Hence No 1 = 23 * 13, No2 = 23 *14.
Hence, 23*14 is the largest Number.
Hasnat Azim said:
5 years ago
We know,
LCM*HCF = N1*N2.
Given,
HCF = 23 & LCM= 23*13*14.
Now,
N1*N2= (23*X) * (23*Y).
23*23*13*14= 23*23*X*Y.
X*Y=14*13.
So, N1= 23*14= 322.
LCM*HCF = N1*N2.
Given,
HCF = 23 & LCM= 23*13*14.
Now,
N1*N2= (23*X) * (23*Y).
23*23*13*14= 23*23*X*Y.
X*Y=14*13.
So, N1= 23*14= 322.
(5)
Ishu said:
1 decade ago
Why l.c.m is a multiple of uncommon factors? if we take l.c.m of 2,4,6 then its l.c.m is 2*2*3=12 but when we multiply the uncommon factors i.e 2*3=6.
Mahendra said:
8 years ago
I think,
1st no can be 23 and 2nd will 23 * 13 * 14.
The conditions are satisfied.
But options are irrelevant.
So
2nd possibility
23*13 and 23*14.
1st no can be 23 and 2nd will 23 * 13 * 14.
The conditions are satisfied.
But options are irrelevant.
So
2nd possibility
23*13 and 23*14.
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