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.

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.

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..

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)

Well Said, Thanks @Lahari.

1. We know that the HCF of a prime number (when it same i.e. 23 and 23) so the HCF of 23, and 23 is 23 ok.

2. Then in question there is no LCM but here we know that the LCM will be the same as HCF when we are talking about the LCM of 23 and 23. So LCM is 23.

3. But there is a problem that 23 can not be divided by 13 and 14, hence they are not the factors of 23.

But I say they are not the factors but we make 13 and 14 factors of 23 by multiplying them with 23 ok so let's do it. 23'*13=299, 23'-14=322. Then check 13 and 14 completely divided 299 and 322.

Clearly explained. Thank you @Vijay Pandey.

@Chiya.

Good explained. Thanks.