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 4 of 10.
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.
Shivang Dwivedi said:
2 years ago
@Veerbhadra.
Because (12*13, 13) and (13, 12*13) are considered as one unique pair, irrespective of the order of writing.
Because (12*13, 13) and (13, 12*13) are considered as one unique pair, irrespective of the order of writing.
(2)
Siva said:
1 decade ago
@Arvind, you must not consider (26, 78) because then the HCF will become 26; as given in the question HCF must be only 13.
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)
Giri said:
1 decade ago
2 and 6 r not co-primes bcoz 6 has 2 as factor
whereas for 3 and 4 have no common factors except 1
whereas for 3 and 4 have no common factors except 1
RAHUL KUMAR SARASWAT said:
1 decade ago
Sir we have a formula that the product of two numbers= LCM * HCM.
Why this formula is not used in this question ?
Why this formula is not used in this question ?
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.
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?
Then how it is written that a*b=12?
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.
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)
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