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:
1
2
3
4
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 5 of 10.

Vishal said:   8 years ago
4 is not a co-prime because it has a factor 1*4 and 2*2 also.

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.

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.

Gokul said:   7 years ago
xy=2028/13=156.

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.

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.

Subham said:   6 years ago
The factors that is said to be co prime only when their GSF OR HCF is 1.

Veena said:   1 decade ago
@vaani
In the given problem the H.C.F is 13..so if take the pair other than co-prime(i.e., the pair 2,6)....the H.C.F will become 26...but when we take the pairs 1,12;3,4....there is no common factor other than 1.. so that we have to take the pair of co-primes....

Swati said:   1 decade ago
Hey 13a*13b=2028 then a*b=156 if we take 13 common and divide it by 2028.

Then how it is written that a*b=12?

Priya said:   1 decade ago
Factors of:
6 = 1, 2, 3.
2 = 1, 2.

They have highest common factor 2. coprime are those pair that have 1 as hcf.

So only (1,12) and (4,3) are such pairs.


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