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 5 of 16.
Vara said:
1 decade ago
We know that product of two numbers = H.C.F*L.C.M.
X*Y = H.C.F*L.C.M.
In the question they gave H.C.F of two numbers is 23. And the factors of their L.C.M are 13 and 14.
X*Y = H.C.F*L.C.M | check | L.C.M factors.
X*Y = 23*(13*14) |of two no's.
So |X = 23*13 = 299; |23|322, 299 ||14, 13.
Y = 23*14 = 322; ||.
So the greatest among the two no's is 322 |.
X*Y = H.C.F*L.C.M.
In the question they gave H.C.F of two numbers is 23. And the factors of their L.C.M are 13 and 14.
X*Y = H.C.F*L.C.M | check | L.C.M factors.
X*Y = 23*(13*14) |of two no's.
So |X = 23*13 = 299; |23|322, 299 ||14, 13.
Y = 23*14 = 322; ||.
So the greatest among the two no's is 322 |.
Akshay said:
9 years ago
I understood it perfectly.
Here 23 is HCF. So it will also be a factor of LCM. And other two factors are given as 13 and 14 so now lcm will be 13 * 14 * 23. But we want to find numbers. So 1st number will be 23 * 13 because 23 is HCF and 13 is given as the 2nd factor of LCM. And the second number will be 23 * 14.
I hope you guys will understand this.
Here 23 is HCF. So it will also be a factor of LCM. And other two factors are given as 13 and 14 so now lcm will be 13 * 14 * 23. But we want to find numbers. So 1st number will be 23 * 13 because 23 is HCF and 13 is given as the 2nd factor of LCM. And the second number will be 23 * 14.
I hope you guys will understand this.
Dheeraj said:
1 decade ago
Let the two numbers be a,b.
HCF(a,b) is always a factor of LCM(a,b). The other two factors of LCM(a,b) are 13 and 14. Therefore the three factors of LCM(a,b) are 23, 13, 14.
LCM(a,b)=LCM(13,14,23)=13*14*23.
Now HCF(a,b)*LCM(a,b)=a*b
23*(23*13*14)=a*b, Therefore bigger number=23*14 and smaller number=23*13 (Since 23 is a common factor of both numbers).
HCF(a,b) is always a factor of LCM(a,b). The other two factors of LCM(a,b) are 13 and 14. Therefore the three factors of LCM(a,b) are 23, 13, 14.
LCM(a,b)=LCM(13,14,23)=13*14*23.
Now HCF(a,b)*LCM(a,b)=a*b
23*(23*13*14)=a*b, Therefore bigger number=23*14 and smaller number=23*13 (Since 23 is a common factor of both numbers).
Always krishna said:
1 year ago
HCF of two numbers is the number which is the common factor for both numbers given Here 23 is the common factor.
Other than this common factor, we also will have the product of uncommon factors for the two numbers (13 and 14 here).
The first number = 23 × 13 = 299 and
secondly number =23 × 14 = 322,
The greatest of two numbers is 23×14 = 322.
Other than this common factor, we also will have the product of uncommon factors for the two numbers (13 and 14 here).
The first number = 23 × 13 = 299 and
secondly number =23 × 14 = 322,
The greatest of two numbers is 23×14 = 322.
(46)
Lalitha said:
1 decade ago
What chiya said is totally wrong
(H.C.F)*(L.C.M)=a*b this is right but
Chiya said: (Fri, Apr 22, 2011 02:18:39 AM)
HCF*LCM=a*b
23*(13*14)=a*b
(23*13)*(23*14)=a*b
a=23*13
b=23*14
Therefore b = 23*14 is the greatest.
23*(13*14)=a*b
(23*13)*(23*14)=a*b This is wrong.
Answer is right but logic is wrong. Anybody explain it clearly ?
(H.C.F)*(L.C.M)=a*b this is right but
Chiya said: (Fri, Apr 22, 2011 02:18:39 AM)
HCF*LCM=a*b
23*(13*14)=a*b
(23*13)*(23*14)=a*b
a=23*13
b=23*14
Therefore b = 23*14 is the greatest.
23*(13*14)=a*b
(23*13)*(23*14)=a*b This is wrong.
Answer is right but logic is wrong. Anybody explain it clearly ?
Anoop said:
1 decade ago
Let first number = 23 *a and second number = 23 * b where a and b are the products of the uncommon factors and they will be different numbers.
lcm=23*13*14
that means 23*a*__=23*b*__ = 23 * 13 * 14
a*__ = 13*14
b*__ = 13*14
a and b are two different numbers
so either a=14 & b=13
or a=13 and b = 14
so the numbers are 23*13 and 23 *14
lcm=23*13*14
that means 23*a*__=23*b*__ = 23 * 13 * 14
a*__ = 13*14
b*__ = 13*14
a and b are two different numbers
so either a=14 & b=13
or a=13 and b = 14
so the numbers are 23*13 and 23 *14
Gopakumar V said:
1 decade ago
The answer need not be 23x14. The larger number can be 23x13x14 and the smaller number 23. In this case also HCF will be 23 and LCM will be 23x13x14. Only statement is the factors of LCM are 23,13 & 14. I think we cannot conclude the answer unless one of the numbers is clearly stated in the question. Please correct if I am wrong.
Shahnawaz said:
7 years ago
Here, 'other two factors of their lcm should be taken into consideration carefully.
Suppose there are two numbers, 15 and 25.Its hcf is 5 and lcm is 75.now write its factors.. 3*5*5, among these factors one of three is hcf, so when we multiply by its hcf with remaining other two factors i.e 5*3 and 5*5 gives original number.
Suppose there are two numbers, 15 and 25.Its hcf is 5 and lcm is 75.now write its factors.. 3*5*5, among these factors one of three is hcf, so when we multiply by its hcf with remaining other two factors i.e 5*3 and 5*5 gives original number.
Sairam said:
1 decade ago
H.C.F of two numbers is 23(which is a common factor for both).
So the two numbers will be 23X , 23Y.
L.C.M*H.C.F = 23X*23Y.
Therefore L.C.M will be 23*x*y.
But the other two factors given are 13, 14.
So x will be 13 and y will be 14.
The numbers are 23X, 23Y which are 23*13, 23*14.
The greatest number is 23*14 = 322.
So the two numbers will be 23X , 23Y.
L.C.M*H.C.F = 23X*23Y.
Therefore L.C.M will be 23*x*y.
But the other two factors given are 13, 14.
So x will be 13 and y will be 14.
The numbers are 23X, 23Y which are 23*13, 23*14.
The greatest number is 23*14 = 322.
Vinay gudipati said:
7 years ago
Given that the HCF of the number is 23 and then given LCM factors of that number is 13 and 14 so we can multiple 23 with the given factors which is given highest value it is the large value and the solution for that problem.
23 * 13=299.
23 * 14=322.
So 322 is the solution according to the problem.
23 * 13=299.
23 * 14=322.
So 322 is the solution according to the problem.
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