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

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.

hcf of any two numbers is a factor of those two numbers .. means example if u take hcf of 12 and 18 .. its 6 .. it means 6 is a factor of 12 and 18. 6*2=12 6*3=18
now if i say there are two numbers in ratio 2:3 whose hcf is 6 how will u write the two numbers ??
solve my question and u will understand it
ans: hcf*2 is one number hcf*3 is the other

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.

Here given two ratios are 3:4 and given HCF is 4 so that's the highest common factor so one can think that could be multiple of 3:4.

So just multiplied with 3*4 and 4*4 so two numbers we get are 12 and 16 take out LCM by 12->2*2*3 and of 16->2*2*2*2-> 2*2*3*2*2->48.

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.

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.

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.........

Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
i understand this step but i dont understand this step he numbers 12 and 16. please explain.

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.

3x ,4x be the two numbers and the given Question HCF is given so take HCF of (3, 4) = 1x.
So x = 4.
3*4=12,
4*4=16,
LCM = 48.