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

Please tell me why use h.c.f value instead of x

hcf * lcm= pro. of no
4*lcm=3x*4x
lcm=3x*4x/4

reply according to this

L.C.M. OF 3 : 4 IS ............. 12
AND THE H.C.F IS GIVEN 4 IN THE QUESTION

NOW , REQUIRED NUMBER IS [12*4] = 48 ANSWER

IS THE WAY IS RIGHT OR NOT.........

Easy and time saving trick is.

3:4= 3*4 = 12.

12*hcf=>>>> 12*4=48 answer.

I understand that assume numbers are 3x & 4x so hcf is x. But now how x is equals to 4?

@Kinjal.

Find out the common multiple of 4&3 you will get the answer.

As nisha said,

a*b = lcm*hcf

3*4 = 4*lcm

We get value lcm = 3.

Why can't we do in this method?

3:4 = 3*4 = 12.

12*HCF = 12*4 = 48.

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.

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.