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 4 of 16.
Raki said:
7 years ago
Suppose LCM.of 4,6 is 12, so here 12 is LCM...but other factors of 12 is (3,4),(6,2).
So the product of factors is 12. so In this problem indirectly LCM given with factors those are (13,14).
So, now use formula LCM * HCF= product of numbers.
LCM(13*14)*HCF(23)= a*b.
Here 182*23=a*b.
2366=a*b...
We can use any of two numbers in this 2366 but HCF 23..Here, we can only take product of 23, so( 23*13),(23*14).
So the product of factors is 12. so In this problem indirectly LCM given with factors those are (13,14).
So, now use formula LCM * HCF= product of numbers.
LCM(13*14)*HCF(23)= a*b.
Here 182*23=a*b.
2366=a*b...
We can use any of two numbers in this 2366 but HCF 23..Here, we can only take product of 23, so( 23*13),(23*14).
Mugil said:
1 decade ago
From my view,
Read the question carefully,already we got h.c.f for two numbers. So,there is no dealing with h.c.f and keep h.c.f aside and change question like this (for your understanding). Find the l.c.m between 23 and 14 and also 23 and 13 and find which has greatest factor?
g.c.f for 23*13 = 299.
g.c.f for 23*14 = 322.
Out of 299 and 322, 322 is the greatest value and hence it is the answer.
Read the question carefully,already we got h.c.f for two numbers. So,there is no dealing with h.c.f and keep h.c.f aside and change question like this (for your understanding). Find the l.c.m between 23 and 14 and also 23 and 13 and find which has greatest factor?
g.c.f for 23*13 = 299.
g.c.f for 23*14 = 322.
Out of 299 and 322, 322 is the greatest value and hence it is the answer.
Sallu said:
1 decade ago
First we have to understand the meaning of factor.
i.e. If number a is divided another number b exactly we say that a is factor of b.
Hence as per this factors are 13 and 14. So to find largest number.
Let us consider x and y are numbers.
x/factor = HCF.
y/factor = HCF.
x/13 = 23, x = 13*23 x = 299.
y/14 = 23, y = 14*23 y = 322.
So largest number is 322. Simple and less time consumption.
i.e. If number a is divided another number b exactly we say that a is factor of b.
Hence as per this factors are 13 and 14. So to find largest number.
Let us consider x and y are numbers.
x/factor = HCF.
y/factor = HCF.
x/13 = 23, x = 13*23 x = 299.
y/14 = 23, y = 14*23 y = 322.
So largest number is 322. Simple and less time consumption.
Anand said:
6 years ago
Here, it is given that HCF of the two numbers are 23.
Similarly factors of LCM are 13 & 14,
Le the numbers be a & b.
We know LCM = 13*a or LCM =14*b (vice versa).
We also know LCM * HCF = a*b.
Here, 1) LCM = 13*a & HCF =23.
So, (13*a) * 23= a*b.
implies, b=23*13!
2) LCM =14*b & HCF =23.
So, (14*b) * 23 =a*b.
Implies a =23*14!
Thus, the Highest number is a= 23*14=322.
Similarly factors of LCM are 13 & 14,
Le the numbers be a & b.
We know LCM = 13*a or LCM =14*b (vice versa).
We also know LCM * HCF = a*b.
Here, 1) LCM = 13*a & HCF =23.
So, (13*a) * 23= a*b.
implies, b=23*13!
2) LCM =14*b & HCF =23.
So, (14*b) * 23 =a*b.
Implies a =23*14!
Thus, the Highest number is a= 23*14=322.
Deepak mahato said:
7 years ago
Here we have 23 which is the HCF (highest common factor) of two no which is unknown to us. now here, also two more factors of the no`s are given 13 and 14.
Now it is easy to calculate those two numbers
23 and 13 are the factors of 23*13=299,
and 23 and 14 are the factors of 23*14=322,
now here HCF= 23 and the larger no=322 which is the answer... Am I right?
Now it is easy to calculate those two numbers
23 and 13 are the factors of 23*13=299,
and 23 and 14 are the factors of 23*14=322,
now here HCF= 23 and the larger no=322 which is the answer... Am I right?
Pranav Shandilya said:
6 years ago
HCF = 23, Factors of LCM = 13 & 14(You can also write 26 & 7)
LCM = 23*13*14 = 23*26*14.
Let a & b be two nos.
a*b = HCF * LCM.
= 23 * 23 * 13 * 14 =23 * 23 * 26 * 7.
Either you get (23*13 & 23*14) or (23*26 & 23*7).
In 1st case:
a = 23*13 = 299 & b = 23*14 = 322.
In 2nd case:
a = 23*26 = 498 & b = 23*7 = 166.
So Greater No is either 322 or 498.
LCM = 23*13*14 = 23*26*14.
Let a & b be two nos.
a*b = HCF * LCM.
= 23 * 23 * 13 * 14 =23 * 23 * 26 * 7.
Either you get (23*13 & 23*14) or (23*26 & 23*7).
In 1st case:
a = 23*13 = 299 & b = 23*14 = 322.
In 2nd case:
a = 23*26 = 498 & b = 23*7 = 166.
So Greater No is either 322 or 498.
Shahriar said:
8 years ago
Let, A and B are the two numbers.
As 23 is the HCF of the two numbers.
We can assume that
a= 23*x, b=23*y, where x and y are the other factors of the numbers.
Now, LCM of a(23*x) and b(23*y) = 23*x*y.
It is given that the other factors of the l.c.m are 13 & 14.
So we can say that x= 13 and y = 14.
Therefore a = 23 * 13,
And b = 23 * 14.
So the larger number is 23*14 = 322.
As 23 is the HCF of the two numbers.
We can assume that
a= 23*x, b=23*y, where x and y are the other factors of the numbers.
Now, LCM of a(23*x) and b(23*y) = 23*x*y.
It is given that the other factors of the l.c.m are 13 & 14.
So we can say that x= 13 and y = 14.
Therefore a = 23 * 13,
And b = 23 * 14.
So the larger number is 23*14 = 322.
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...
Prathyusha said:
1 decade ago
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!.....
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!.....
Ezhil said:
5 years ago
E. G.consider the 2 number are 10 & 15
HCF of these two number is 5.(which is given)
10/5=2 and 15/5=3.
Here 2 and 3 are the least common multiples of 10 and 15.
So, if we have to find the number we will multiply the HCF which is 5 with the Least common Multiples which are 2 and 3. So that we can get the numbers 10 and 15. In that, the highest number is 15..
HCF of these two number is 5.(which is given)
10/5=2 and 15/5=3.
Here 2 and 3 are the least common multiples of 10 and 15.
So, if we have to find the number we will multiply the HCF which is 5 with the Least common Multiples which are 2 and 3. So that we can get the numbers 10 and 15. In that, the highest number is 15..
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