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. 2)
2.
The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
Answer: Option
Explanation:
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Discussion:
153 comments Page 6 of 16.
Tanaya said:
9 years ago
HCF is 23.
LCM is 13 * 14 * 23 (as it is given 13 & 14 are OTHER FACTORS),
Both the numbers have 13 & 14 as their factors, Hence the greater number should be divisible by 14 & the smaller number should be divisible by 13.
The answer is 322 (divisible by 14) as 322 = 23 * 14.
LCM is 13 * 14 * 23 (as it is given 13 & 14 are OTHER FACTORS),
Both the numbers have 13 & 14 as their factors, Hence the greater number should be divisible by 14 & the smaller number should be divisible by 13.
The answer is 322 (divisible by 14) as 322 = 23 * 14.
Rajesh said:
1 decade ago
Read the question clearly.
Given that the two factors is 13 and 14 this means 23 is also a factor of L.C.M.
So LCM is 23*13*14.
Now 23 is HCF so suppose two numbers are 23*x and 23*y.
By theorem; (23*x)(23*y) = (23)(23*13*14).
This gives x equal to either 13 or 14 and similarly y.
Given that the two factors is 13 and 14 this means 23 is also a factor of L.C.M.
So LCM is 23*13*14.
Now 23 is HCF so suppose two numbers are 23*x and 23*y.
By theorem; (23*x)(23*y) = (23)(23*13*14).
This gives x equal to either 13 or 14 and similarly y.
Poornima said:
1 decade ago
HCF- Higest Common Factor, so we already have one factor of the number we need to find out ok. N we are also given the least common factors ie, 13 n 14. So to get the numbers just multiply both the Least common numbers with their HCF so that you can find the actual numbers.
C T said:
9 years ago
Let Nos: x, y.
HCF = 23.
Other two factors of their L.C.M are 13 and 14 => x13 = LCM, y14 = LCM.
We know HCF *LCM = Product of Nos.
23 * x13 = xy = 23 * y14.
Take 1st pair, 23 * x13 = xy which gives y = 23 * 13.
2nd pair xy = 23 * 14.
x = 23 * 14 = 322 Highest.
HCF = 23.
Other two factors of their L.C.M are 13 and 14 => x13 = LCM, y14 = LCM.
We know HCF *LCM = Product of Nos.
23 * x13 = xy = 23 * y14.
Take 1st pair, 23 * x13 = xy which gives y = 23 * 13.
2nd pair xy = 23 * 14.
x = 23 * 14 = 322 Highest.
Pavan said:
1 decade ago
I would like to solve this problem by using factors concept.
Here given least common multiple so we can write this numbers as 13:14.
This ratio are least parts of this numbers.
And hcf is given as 23 means highest parts 23.
So this numbers we can write as 23*13, 23*14.
Here given least common multiple so we can write this numbers as 13:14.
This ratio are least parts of this numbers.
And hcf is given as 23 means highest parts 23.
So this numbers we can write as 23*13, 23*14.
Ranbir Singh said:
8 years ago
We can represent any integer number in the form of: pq+r.
Where p is dividend, q is quotient, r is reminder.
So: A = pq1 + r;
B = pq2 + r;
HERE P=23 (HCF GIVEN).
LCM FACTOR GIVEN ,SO q1 =13,q2 =14 , REMAINDER (r=0).
So, A = 23*13 = 299 , B= 23*14= 322.
ANSWER = 322.
Where p is dividend, q is quotient, r is reminder.
So: A = pq1 + r;
B = pq2 + r;
HERE P=23 (HCF GIVEN).
LCM FACTOR GIVEN ,SO q1 =13,q2 =14 , REMAINDER (r=0).
So, A = 23*13 = 299 , B= 23*14= 322.
ANSWER = 322.
Lahari said:
5 years ago
Let us take two numbers as A and B.
Their HCF is 23(prime).
And their LCM is 13 and 14.
Every number is the resultant product of their HCF and LCM.SO,consider a*b=23*(13*14)
(Observe the question it's given as their LCM and their HCF).
Then a = 23*13.
And b = 23*14.
Their HCF is 23(prime).
And their LCM is 13 and 14.
Every number is the resultant product of their HCF and LCM.SO,consider a*b=23*(13*14)
(Observe the question it's given as their LCM and their HCF).
Then a = 23*13.
And b = 23*14.
(3)
Mohit said:
1 decade ago
23 is common in both.
13 and 14 are factors of lcm thus may be common or may occur separate in both number but if they were commen then they should be included into hcf and that is not so.
Therefore 13 and 14 comes separately in both number.
Thus 23*13 and 23*14.
13 and 14 are factors of lcm thus may be common or may occur separate in both number but if they were commen then they should be included into hcf and that is not so.
Therefore 13 and 14 comes separately in both number.
Thus 23*13 and 23*14.
AVINASH said:
1 decade ago
What pratyusha said is h.c.f of two numbers that means common factor of two numbers is 23.
Hope there are more than common factors..
then what about uncommon factors..they given lcm of two factors..is uncommon factors are lcm of factors?
I want clear explanation
Hope there are more than common factors..
then what about uncommon factors..they given lcm of two factors..is uncommon factors are lcm of factors?
I want clear explanation
Maswood Khan said:
7 years ago
if A and B are the Numbers,
let x = HCF(A,B) then,
LCM(A,B) = x * A/x * B/x.
In question they have given the other two factor of LCM as 13 and 14, we don't need first factor because we already know it's 23(HCF of Number).
So we can say -
A = 23*13.
B = 23*14.
let x = HCF(A,B) then,
LCM(A,B) = x * A/x * B/x.
In question they have given the other two factor of LCM as 13 and 14, we don't need first factor because we already know it's 23(HCF of Number).
So we can say -
A = 23*13.
B = 23*14.
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