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

I think,

1st no can be 23 and 2nd will 23 * 13 * 14.
The conditions are satisfied.
But options are irrelevant.
So
2nd possibility
23*13 and 23*14.

Guys, Let's understand it by set theory. We have set A={a,b,c,d} & B={e,b,c,f,g}.and in this question abcd are factors of A and ebcfg are factors of B.

So hcf will be b.c and that's common in both factors.If we say lcm of A, B then It will contain b,c as common part of their lcm({b,c}, adefg) where ad belongs to A and efg belongs to B and we will call them uncommon or other factors of their lcm.and you know that how are they used to get a particular no.A or B. You can take ad as 13 and efg as 14.

So, lcm will be 23 .13.14 and hcf will be 23 and no.A is 23.13 and B is 23.14.

Yes, you are right @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.

Thanks for the given solution @Chiya.

Thanks @Sameera.

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

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

Thanks @Vijay Pandey.

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.