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 2 of 10.
Madhu said:
4 years ago
(2, 6) are not co prime numbers.
As.
2=1*2.
6=1*6, 2*3;.
So for 6. (2) is again a factor so they can't be.
As.
2=1*2.
6=1*6, 2*3;.
So for 6. (2) is again a factor so they can't be.
(1)
Nikhil G said:
5 years ago
@All.
1*12 = 1*3*2*2.
12*1 = 1*3*2*2.
2*6 = 3*2*2.
6*2 = 3*2*2.
3*4 = 3*2*2.
4*3 = 3*2*2.
So possible pairs are only 2.
1*12 = 1*3*2*2.
12*1 = 1*3*2*2.
2*6 = 3*2*2.
6*2 = 3*2*2.
3*4 = 3*2*2.
4*3 = 3*2*2.
So possible pairs are only 2.
(8)
Veerabhadra said:
5 years ago
Why not answer is 4?
(1*13, 12*13) (3*13, 4*13) (12*13, 1*13) (4*13, 3*13) these are four possible pairs.
(1*13, 12*13) (3*13, 4*13) (12*13, 1*13) (4*13, 3*13) these are four possible pairs.
(1)
Chaitanya said:
5 years ago
Take 13x*13y( because HCF is 13)
Let 13x*13y=2028
xy=2028/13*13
xy becomes 12.
Next find out the coprimes which should be the form of x,y hence,
coprimes are (1,12) and (3,4)or (4,3),
so the real pair will be;
(13*1,13*12)and (13*3,13*4),
Hence the answer is 2.
Let 13x*13y=2028
xy=2028/13*13
xy becomes 12.
Next find out the coprimes which should be the form of x,y hence,
coprimes are (1,12) and (3,4)or (4,3),
so the real pair will be;
(13*1,13*12)and (13*3,13*4),
Hence the answer is 2.
(1)
Subham said:
5 years ago
The factors that is said to be co prime only when their GSF OR HCF is 1.
Umesh said:
5 years ago
The answer is incorrect. The answer could also be 2 and 6.
Randy Ranjith said:
6 years ago
Then why we take (4, 3) 4 is not co-prime?
(1)
Julie said:
6 years ago
Thank you for giving the clear answer @Snehesh.
(1)
Shahrukh said:
6 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)
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.
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