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

I understood it perfectly.

Here 23 is HCF. So it will also be a factor of LCM. And other two factors are given as 13 and 14 so now lcm will be 13 * 14 * 23. But we want to find numbers. So 1st number will be 23 * 13 because 23 is HCF and 13 is given as the 2nd factor of LCM. And the second number will be 23 * 14.

I hope you guys will understand this.

Let us say, the two numbers are: 23 x a and 23 x b.

Why? because 23 is the highest common " factor " of the two numbers. If you still don't understand why Study the concept of factors properly.

Now we know that,

"H.C.F is one of the factors of L.C.M". (That's why in the question they have mentioned, " the 'other two' factors are 13 and 14. That means the three factors of LCM are 23, 14, 13)" .

Therefore LCM = 23 x 14 x 13.

Now we know that, " Product of two numbers = Product of their H.C.F. and L.C.M ".
Therefore, (23 x a) x (23 x b) = 23 x 23 x 14 x 13.
Therefore, a x b = 14 x 13.
Therefore, a x b = 2 x 7 x 13.

Now there are more than one values possible for a and b which satisfy the above equation. But, only if we use a = 14 and b = 13 for the two numbers (23xa and 23xb), we will get the HCF = 23. For all other values of a and b, we won't get 23 as the HCF. Try it!

Therefore, The two numbers are 23 x 14 and 23 x 13.

Hope it is clear now!

There should be given in the question that one factor is 14 and 13 is the another factor number.

Because, If the no. are x and y,
We can take two conditions according to question;

Condition 1:

x = 23 * 14.
y = 23 * 13 .

Condition 2:

x = 23 * 1
y = 23 * 14 * 1.

Then the only lcm will be 23 * 14 * 13, and then only you can write in the question that 14 and 13 are other two factors.

According to this question, the answer can be;

1)
x = 23*14.
y = 23*13.
So in this 23 * 14 will be greater.

2)
x = 23.
y = 23 * 13 * 14.

So, 23 * 13 * 14 will be greater.

According to me, the question is not complete and to complete it read my first line.

Hope you understand my explanation, Thankyou.

We have the terms HCF, LCM, product of 2 numbers (numbers be a,b).

In general,
Number = Factor * Factor.

eg :
6= 2*3 ----> 2, 3 factors of number 6.
8= 2*4-----> 2, 4 factors of 8.

So,
a = Factor * Factor.
b = Factor * Factor.

Here the 2 factors are 13, 14.

Given that, the highest common factor is 23,
So, we got another factor 23.

We require 4 factors to get a & b. But we have only 3.
And clearly said 23 is highest common factor.

Where 23 is a common factor in both a & b.

a = 23 * 13.
b = 23 * 14.

Therefore, the larger number = (23 x 14) = 322.

Hope you all understand this, if any mistake correct me.

I am confused with the question and method of solution. Can anyone help me?

Dear Friends,

Still I didn't understand the concept of LCM & HCF.

Please explain me in an easy way.

I'm little bit confuse in this concept. How we know to solve this ways. Please anybody is there to clear my doubt.

Please clear the concept easily.

Answer which is explained above assumes that the extra factors 13 and 14 are included in two separate numbers. The question does not say anything of this sort.

So technically, the correct answer is n1 = 23 and n2 = 23 x 13 x 14 = 4186.

You can verify that HCF = 23 and LCM = 2 x 7 x 13 x 23 = (2 x 7) x 13 x 23, for which the given statement that "The other two factors included in the LCM are 13 and 14" is perfectly valid.

HCF means highest common factor.

LCM means least common Multiple.

Both are different. In this question they have given HCF of two numbers are 23.

Let us consider x and y as two no's then HCF (x, y) = 23.

We don't know the value of x and y. Then LCM of the two nos have factors 13 and 14.

This means that LCM (x, y) = z.

The value z have factors 13 and 14 which will divide z without leaving a remainder.

The main question is finding the larger of the two no is? That means we have to find biggest value among x and y.

I have understood the question but I don't how to solve it. I need clear explanation please.