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

Not getting this. Please can anybody explain me clearly?

Statement 1:- We know that if 2 numbers are co-primes, then their LCM is equal to their product.
Statement 2:- We also know that if 2 numbers are co-primes,then their HCF is 1.

In the given question, 13 and 14 are the factors of the LCM of 2 numbers. Therefore it is understood that the 2 numbers are the multiples of 13 and 14.

23 is the HCF of 2 numbers. Therefore 2 numbers are not co-primes.
Given that 23 is the common factor of the 2 numbers - 23x13 = 299 and 23 x 14 = 322.
LCM of 299 and 322 = 4186.13 and 14 are the factors of 4186.
HCF of 299 and 322 = 23.
Therefore, 23 x 14 = 322 is the highest number.

@Ramesh.

We know that all the factors of the number A are also the factors of all the multiples of the number A.
In the given problem, 13 and 14 are factors of the Least Common Multiple of 2 numbers, therefore 13 and 14 are also considered as factors of the two numbers.
The HCF of 2 numbers = 23.
Therefore the required numbers are 23 x 13 = 299 and 23 x 14 = 322.
Therefore 23x14=322 is the highest number.
HCF of 299 and 322 = 23,
LCM of 299 and 322 = 4186.
13 and 14 are the factors of 4186.

In my view, x and why are given two numbers.

Hcf of (x, y) =23;.
Lcm of (x, y) =13, 14;.

We know that;

Hcf x lcm=X x Y.
So, 23x13=299;.

23 x 14 =322 which is larger so 322 is the answer.

If any mistakes correct me.

Thanks @Vijay Pandey.

HCF * LCM
X * Y=. 23 * 13 =299.
X * Y= 23 * 14 =322 large.

Simple and easy method to understand the solution. Thanks @Sanjeev Goel.

Thanks @Sameera.

Thanks for the given solution @Chiya.

Let, A and B are the two numbers.

As 23 is the HCF of the two numbers.
We can assume that
a= 23*x, b=23*y, where x and y are the other factors of the numbers.
Now, LCM of a(23*x) and b(23*y) = 23*x*y.
It is given that the other factors of the l.c.m are 13 & 14.
So we can say that x= 13 and y = 14.

Therefore a = 23 * 13,
And b = 23 * 14.
So the larger number is 23*14 = 322.