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 8 of 10.
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.
Gokul said:
7 years ago
xy=2028/13=156.
Then how to solve it?
Then how to solve it?
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.
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.
(9)
Zoha said:
7 years ago
The product of two numbers is 2028 and their HCF is 13 find their LCM.
Ans: so, there LCM is 2 is that correct.
Ans: so, there LCM is 2 is that correct.
Shahrukh said:
7 years ago
If 13x * 13y = 2028 then;
It should have been 13(x*y)= 2028
And x*y= 156
But your solution is telling that
13*13(x*y)= 2028.
x*y = 2028/ 169 = 12.
So , x*y = 12.
I mean why divided by 169 why not by 13 after taking common 13? Please tell me.
It should have been 13(x*y)= 2028
And x*y= 156
But your solution is telling that
13*13(x*y)= 2028.
x*y = 2028/ 169 = 12.
So , x*y = 12.
I mean why divided by 169 why not by 13 after taking common 13? Please tell me.
(11)
Julie said:
6 years ago
Thank you for giving the clear answer @Snehesh.
(1)
Randy Ranjith said:
6 years ago
Then why we take (4, 3) 4 is not co-prime?
(1)
Umesh said:
5 years ago
The answer is incorrect. The answer could also be 2 and 6.
Subham said:
5 years ago
The factors that is said to be co prime only when their GSF OR HCF is 1.
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