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 3 of 16.
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...
Vinay said:
1 decade ago
Not convinced, please try to give some more practical sollutions, which is easy to understand.
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).
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.
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.
Darknight said:
1 decade ago
Let &b r 2 nos.
NOW HCF*LCM=a*b
13 &14 are two factors of lcm ok
now lcm=a*13 (by defination of lcm && in the question it is given that there r 2 factors)
sim. lcm=b*14
23*lcm=a*b
23*a*13=a*b
so clearly b=23*13
a=23*13
solved!!!!
NOW HCF*LCM=a*b
13 &14 are two factors of lcm ok
now lcm=a*13 (by defination of lcm && in the question it is given that there r 2 factors)
sim. lcm=b*14
23*lcm=a*b
23*a*13=a*b
so clearly b=23*13
a=23*13
solved!!!!
Sugandh said:
1 decade ago
@Chiya explains good.
Siraj said:
1 decade ago
@Chiya a*(b*c) is not equal to (a*b)*(b*c).... :D
Siraj said:
1 decade ago
@Neha you are right. , how can we multiply 23 twice, I think Darknight's explanation is good. ,
Tej said:
1 decade ago
Product of l.c.m and h.cf is that numbers so in the same way hcf is 23 and l.cm 13 and 4 are given and ther the ans 23*14 is right
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