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 5 of 10.
Yash Srivastava said:
1 decade ago
HCF of 26 and 78 is 2 not 13.
Deepika said:
1 decade ago
Can anyone explain in a simple way?
Naheem sheikh said:
1 decade ago
x*y = 2028.
x*13 = 2028.
x = 156.
Factor = 13*12.
Now, please explain? Anyone in details?
x*13 = 2028.
x = 156.
Factor = 13*12.
Now, please explain? Anyone in details?
Deepak said:
1 decade ago
4 is definitely not prime number, then why you have taken as co prime?
Only one pair can be done i.e. 13, 1.
Only one pair can be done i.e. 13, 1.
Himank said:
10 years ago
@Naheem.
According to the formula.
Product = HCF*LCM.
Product is given 2028.
And HCF is 13.
So we get LCM = 2028/13 = 156.
Now factors of 156 is calculated which comes out to be 2*2*3*13.
According to the formula.
Product = HCF*LCM.
Product is given 2028.
And HCF is 13.
So we get LCM = 2028/13 = 156.
Now factors of 156 is calculated which comes out to be 2*2*3*13.
Priya said:
10 years ago
I am not getting the concept of ab=12?
How it came an some one please explain?
How it came an some one please explain?
Sai said:
10 years ago
13a*13b = 2028.
169ab = 2028.
ab = 12.
169ab = 2028.
ab = 12.
Subbu said:
10 years ago
I am not getting the concept of ab=12.
Xing said:
10 years ago
Longer method, divide both side by 13.
=> 13a * 13b/13 = 2028/13.
=> 13a * b = 156.
=> ab = 156/13.
=> ab = 12.
=> 13a * 13b/13 = 2028/13.
=> 13a * b = 156.
=> ab = 156/13.
=> ab = 12.
(1)
Vinay ambidi said:
10 years ago
No someone asked why 5, 7 but if we multiply those numbers we will get 5*7 = 35.
That's why we have to take 1, 12 or 3, 4.
That's why we have to take 1, 12 or 3, 4.
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