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

Initially let the two numbers be 3x and 4x and there given h.c.f is 4.

So that means 3*x and 4*x are the product of a number and a variable which is = to the product of h.c.f and l.c.m as we know.now h.c.f given here is 4.

So put 4 instead of x and get the numbers i.e 12 and 16.

Find the l.c.m of these two numbers i.e 48.

Excellent information.

3x = 3 (4 H.C.F) = 12.
4x = 4 (4 H.C.F) = 16.

LCM of 12 & 16.

12 = 2*2*3.
16 = 2*2*2*2.

Now we have 2*2*3*2*2*2*2 = 192.

HCF = 4/LCM 192.

4/192 = 48 answer.

Got it or not.

You can't get 48 by 4/192 you can get 48 by 192/4.

Let the numbers be 3x and 4x.

We know that 3x*4x = HCF*LCM.

=> 12x^2 = 4*LCM.

=> LCM = 3x^2.....equation (1).

L.C.M. of 3x, 4x = 12x.....equation (2).

Now, equation(1) = equation(2).

=> 3x^2 = 12x.

=> x = 4.

=> L.C.M = 12x = 12*4 = 48.

Thanks.

HCF = 4 (given).
Say m = 4.

LCM = Product of two numbers/HCF.

= 3m*4m/m.
= 12*16/4.
= 48.

The product of two numbers is 724 and HCF is 4 then find the LCM?

The sum of two number is 420 and one of them is 260. Find the product of the two numbers.

Find the greatest number of 4 digits which is divisible by 35.

Since the ratio is given and the HCF as well, we now know that there will not be any other factor other than the ratio * HCF for both the numbers. Because if there are any more factors then the HCF will increase by that number. So the two numbers have to be 3*HCF and 4*HCF.

Eg: Suppose we say that HCF is not the only other factor than the number could be 3*HCF*x and 4*HCF*Y, now for the ratio to be 3:4, x = why. But x=why then we have another common factor for the two numbers and the HCF would then be HCF*x which is not true as per the given question. Thus, there should be no other common factor. Thus, we can say whenever the ratio and HCF are given the numbers are always ratio * HCF.

The product of HCF 18 and LCM 16 is?

Can anyone help to get the answer?