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. 9)
9.
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
Answer: Option
Explanation:
Let the numbers 13a and 13b.
Then, 13a x 13b = 2028
ab = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).
Clearly, there are 2 such pairs.
Discussion:
94 comments Page 3 of 10.
Jagrati said:
7 years ago
Product of 2 numbers = HCF * LCM.
2028= 13 * LCM.
2028/13=LCM.
Since, LCM=156.
Factors of 156 are 2*2*39.
That is the pair is 2.
2028= 13 * LCM.
2028/13=LCM.
Since, LCM=156.
Factors of 156 are 2*2*39.
That is the pair is 2.
(8)
Abhishek s g said:
7 years ago
We should not take 2 and 6 because if we take 2 and 6, the product will be 2028 but HCF is 26 not 13.
Gokul said:
7 years ago
xy=2028/13=156.
Then how to solve it?
Then how to solve it?
Mahesh said:
7 years ago
If we take 2 and 6 then we get (13*2)*(13*6)=26*78.
HCF of 26 and 78 will be 26 it's against the given question.
When we took 3 and 4 we get HCF as 13 only.
That's the reason why we shouldn't take 2 and 6.
HCF of 26 and 78 will be 26 it's against the given question.
When we took 3 and 4 we get HCF as 13 only.
That's the reason why we shouldn't take 2 and 6.
Shubham said:
8 years ago
ab=12, now possible solutions can be 1*12, 3*4, 2*6 but we won't consider 2*6 because it will lead to HCF 13*2, as 2 is a factor of both 2 & 6. Hope you get it.
Vishal said:
8 years ago
4 is not a co-prime because it has a factor 1*4 and 2*2 also.
Nagendra said:
8 years ago
In the question, they doesn't mention about the co-prime numbers, right?
Kishan said:
8 years ago
The product of two numbers is 2028 and their HCF is 13 If the numbers of two digits find the numbers.
Can anyone answer me?
Can anyone answer me?
Shivangi said:
8 years ago
But Question is how many no of the pair. Not co factors. Please clear my doubt is no of pair means co-factor?
Balachandra Padiyar said:
8 years ago
The co prime numbers those numbers which are having only one common factor that is 1
in (2&6) the factors are,
2 = 1,2.
6 = 1,2,3.
Here in 2&6 there are two factors ie, 1&2 hence they are not co primes hence it can't be used here.
Let us take 4&3,
4=1,2,4,
3=1,3,
Here only one common factor ie,1 and same for 12&1.
in (2&6) the factors are,
2 = 1,2.
6 = 1,2,3.
Here in 2&6 there are two factors ie, 1&2 hence they are not co primes hence it can't be used here.
Let us take 4&3,
4=1,2,4,
3=1,3,
Here only one common factor ie,1 and same for 12&1.
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