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

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.

HCF of 2 numbers equal to the highest of all the common factors of the two numbers
23 is the common factor of the two numbers.

Let 23 x,23 Y be the two numbers.
we know that the factor of any two numbers is also a factor of the LCM of those two numbers.
So 23 is a factor of the two numbers 23 x and 23 y.
LCM of two numbers.
23 x and 23 Y = 13* 14 *23.

LCM =13*14 *23,
And HCF = 23,
We know that,
LCM * HCF = product of the two numbers,
13 *14 * 23 =23 x * 23 y.
@x*y= 13* 14.

Which shows that larger number will be 14 * 23 that is equal to 322.

Clearly explained. Thank you @Vijay Pandey.

Number 1 = a * 23
number 2 = b * 23
And other factors of LCM are 13 and 14
So clearly a * b = 13 * 14

But my point is:
a * b = 26 * 7
a * b = 81 * 2
As they are co prime in themselves,
So why is the answer not 23*81? Please explain.

@Chiya.

Good explained. Thanks.

@Ahmed.

Yeah, right, good explanation. Thanks.

Please correct me if I am wrong:

Let two numbers be A and B. It is given that their HCF is 23. Therefore, A = 23 * x
and B = 23 * y, where x and y are any integers.

And we can find their LCM as follows: LCM(A, B) = 23 * x * y.

Therefore, x and y are the other two factors of LCM, and we are given that those 2 factors are 13 and 14 respectively.

Therefore x = 13 and y = 14. And hence largest number = 23 * 14 = 322.

Thanks alot. @Dheeraj.

Thank you for explaining the answer @Krishna.