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

@ALL.

48/2 = 24,
48/3 = 16,
Then, 24+16 = 40.

Thanks!

Let the numbers be equal to= k.
the ratio is given as= 2:3.
1st num = 2k.
2nd num = 3k.

Now find their lcm as we find for every number so factors will be= 2 x3 x k =6k.
but in question, the lcm of numbers is given as 48.
that is LCM(of 2k,3k)= 48.
but we found that LCM is 6k.

Thus,
48 = 6k.
k = 48/6,
k = 8.

Now put the value of k for 1st num and second num to find the numbers and we get:-

1st num = 2(8) = 16,
2nd num = 3(8) = 24.

now sum = 16 + 24 = 40.

Hence 40 is the answer.

By Heat and trail method:

48/2 = 24
48/3 = 16.
24 and 16 are those two numbers and sum of these two number is 24+16 = 40.

By general Rule -:
1st number * 2nd number = HCF * LCM.
we have LCM = 48 ;
LCM = ( 1st no * 2nd no)/ HCF.
let HCF = X.

Then 1st number = 2x and,
2nd number = 3x.
so,
48 = (2X * 3X)/X.
(6X^2 ) / X = 48
Then, ,6X = 48,
X = 48/6 = 8.
So, the first number is 2X = 2 * 8 = 16
second number is 3X = 3 * 8 = 24.
Sum of those number is 16 + 24 = 40.

Other method:
We have LCM = 48.
let these two numbers are 2X and 3X.
L.C.M. of 2X and 3X is 6X.
If you do LCM we got X,2,3 multiple of these number is 6X.
So,
6X = 48,
X = 48/6 = 8.

The numbers are 16 and 24.
sum is 40.
That's all.
Thanks

How the LCM of 2x, 3x = 6x? Explain please.

Best method;
Ratio = 2:3.
So, let the numbers be 2x and 3x respectively.
Sum = 2x + 3x = 5x.
=> Sum is MULTIPLE OF 5.

There is only one option which is a MULTIPLE of 5. So 40 is the answer.

Let say we need to find LCM of 2x and 3x;

So.
--- 2x 3x
x | 2 | 3
2 | 1 | 3
3 | 1 | 1
multiply 2 * 3 * x = 6x.

@Ambi.

It's so simple,
Then x of HCF and x in 6x^2 gets cancelled.
And hence 6x is remained.

Very simple way, 2:3 means sum is always a multiple of 5. Here only multiple of 5 is 40.

Simple way.

48/2 = 24.
48/3 = 16.
24 + 16 = 40.

Product of two number = Product of HCF and LCM.

Here we go to solve problem:

48 = x*{3*2}.
48/6 = x.
x = 8.

3x:2x = 3*8:2*8.

1st number 24:2nd number 16.

= 40.