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

LCM*HCF = Value of that number.

So, HCF(LCM1) = n1.

HCF*LCM2 = n2.

So 23*13 = n1.

23*14 = n2.

N1<N2.

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.

Very good explanations.

Read the question clearly.

Given that the two factors is 13 and 14 this means 23 is also a factor of L.C.M.

So LCM is 23*13*14.

Now 23 is HCF so suppose two numbers are 23*x and 23*y.

By theorem; (23*x)(23*y) = (23)(23*13*14).

This gives x equal to either 13 or 14 and similarly y.

Let 'a' and 'b' be the two numbers.

HCF (a, b) = 23.

LCM (a, b) = 13*a = 14*b (or) LCM = 14*a = 13*b.

Note : The (or) case is just to indicate that we could have taken the factors the other way round ---> since they are factors for LCM. Both cases would result in the same large number.

Theorem: The product of two numbers = a*b = LCM (a, b)*HCF (a, b).

Applying the above theorem here :

=> a*b = HCF (a, b)*LCM (a, b).

=> a*b = 23*(13*a) (or).

Therefore => b = 23*13.

Similarly, a = 23*14.

The largest of the 2 numbers = 23*14 = 322 is the answer.

I just want to know how these 13 and 14 obtained?

The L.C.M Of 2 numbers are (23x13) (23x14).

23x13 = 299, 23x14 = 322, which is largest number = 322.

We know that product of two numbers = H.C.F*L.C.M.

X*Y = H.C.F*L.C.M.

In the question they gave H.C.F of two numbers is 23. And the factors of their L.C.M are 13 and 14.

X*Y = H.C.F*L.C.M | check | L.C.M factors.

X*Y = 23*(13*14) |of two no's.

So |X = 23*13 = 299; |23|322, 299 ||14, 13.

Y = 23*14 = 322; ||.

So the greatest among the two no's is 322 |.

We mean (Number = H.C.F*L.C.M) it's wrong or not please explain me.

First we have to understand the meaning of factor.

i.e. If number a is divided another number b exactly we say that a is factor of b.

Hence as per this factors are 13 and 14. So to find largest number.
Let us consider x and y are numbers.

x/factor = HCF.
y/factor = HCF.

x/13 = 23, x = 13*23 x = 299.
y/14 = 23, y = 14*23 y = 322.

So largest number is 322. Simple and less time consumption.