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

Hi Guys,

My explanation is lets consider two numbers X, Y.

23 is the HCF of two numbers which means X and Y are exactly divisible by 23 in other words 23 is common factor for both the numbers so we can write X=23 X some value same as Y=23 X some value.

Then second part of the question if you see other remaining factors of LCM are 13 and 14 which means there is no common factors.

23|X , Y
|------
|13, 14

So X=23 X 13 and Y=23 X 14.

Correct me if I am wrong.

Dear all,

Very easy, Let`s see in a different way,

Here in this question, it is given that there are two numbers ( let them be A & B ) whose HCF is 23. It means that both the numbers have the highest common factor as 23. So, we can write A as 23 x m & B as 23 x n, where m & n are some other factors(not common) , Now, in the question it is also given that Other Factors of LCM of those numbers (i.e. Lcm of A & B) is 13 & 14,

So LCM of A & B will be AB,or the same can be written as LCM of (23 x m) & (23 x n) = (23 x m)(23 x n) , where other factors of LCM are m & n(except 23 because 23 is common in A & B) ,but given, that those other factors are 13 & 14. It means m=13,n=14. now it is very cleared that.

LCM of (23 x m) & (23 x n) is (23 x 13)(23 x 14), where larger number is (23 x 14) or 322.

I will explain to you with Example.
Take two numbers 21 & 36.
21 - 7 *3 & 36 - 12 *3.
H.C.F. - 3.
They gave H.C.F. and give two factors of L.C.M. 7 and 12.
Okey now simply apply logic which is greater.

What is the concept behind this solution?

I didn't understand the solution can anybody explain for me.

HCF- Higest Common Factor, so we already have one factor of the number we need to find out ok. N we are also given the least common factors ie, 13 n 14. So to get the numbers just multiply both the Least common numbers with their HCF so that you can find the actual numbers.

Not convinced.

1]HCF of two numbers is the number which is common factor for both numbers given.here 23 is the common factor.

2]other than this common factor ,we also will have the product of uncommon factors for the two numbers (13 and 14 here).

3]the first number =23*13
and second number=23*14

4]greatest of two numbers is definitely 23*14

Correct me if i am wrong please!.....

Now what are these uncommon factors?

I think the two numbers can be 23 and 23x13x14 i e 4186. Is it possible?
Suppose we take two numbers 4 and 24. Their HCF is 4 and LCM is 24. Then the greatest number is 24 itself even though it is the LCM.Am I right?