Aptitude - Problems on H.C.F and L.C.M - Discussion

See for any number there are 1 HCF and 1 LCM.
So remember this formula:

HCF * LCM= N1 + N2.

HCF given 23;
And LCM given 13&14.
1st take 23*13= N1*N2.
Then take 24*14= N1*N2.
HIGHEST IS THE ANSWER.

Dear all,

Very easy, Let`s see in a different way,

Here in this question, it is given that there are two numbers ( let them be A & B ) whose HCF is 23. It means that both the numbers have the highest common factor as 23. So, we can write A as 23 x m & B as 23 x n, where m & n are some other factors(not common) , Now, in the question it is also given that Other Factors of LCM of those numbers (i.e. Lcm of A & B) is 13 & 14,

So LCM of A & B will be AB,or the same can be written as LCM of (23 x m) & (23 x n) = (23 x m)(23 x n) , where other factors of LCM are m & n(except 23 because 23 is common in A & B) ,but given, that those other factors are 13 & 14. It means m=13,n=14. now it is very cleared that.

LCM of (23 x m) & (23 x n) is (23 x 13)(23 x 14), where larger number is (23 x 14) or 322.

Please explain the answer.

Here, it is given that HCF of the two numbers are 23.

Similarly factors of LCM are 13 & 14,
Le the numbers be a & b.
We know LCM = 13*a or LCM =14*b (vice versa).
We also know LCM * HCF = a*b.
Here, 1) LCM = 13*a & HCF =23.
So, (13*a) * 23= a*b.
implies, b=23*13!
2) LCM =14*b & HCF =23.
So, (14*b) * 23 =a*b.
Implies a =23*14!
Thus, the Highest number is a= 23*14=322.

I will explain to you with Example.
Take two numbers 21 & 36.
21 - 7 *3 & 36 - 12 *3.
H.C.F. - 3.
They gave H.C.F. and give two factors of L.C.M. 7 and 12.
Okey now simply apply logic which is greater.

We know,
LCM*HCF = N1*N2.

Given,
HCF = 23 & LCM= 23*13*14.

Now,
N1*N2= (23*X) * (23*Y).
23*23*13*14= 23*23*X*Y.
X*Y=14*13.

So, N1= 23*14= 322.

E. G.consider the 2 number are 10 & 15
HCF of these two number is 5.(which is given)
10/5=2 and 15/5=3.

Here 2 and 3 are the least common multiples of 10 and 15.

So, if we have to find the number we will multiply the HCF which is 5 with the Least common Multiples which are 2 and 3. So that we can get the numbers 10 and 15. In that, the highest number is 15..

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.

The greatest possibel number is 26*23 that satisfies the conditions. So the given answer is correct.

Answer: Larger Number can be 23*14*13)