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

Hcf = product/lcm.
= 3*4+4*4/4.
= 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.

4 * lcm=3x * 4x.
4 * lcm=3 * 4 * 4 * 4,
Lcm = 12 * 16 ÷ 4.
= 48 -> Is this correct?

Why they put x = 4? Explain me.

@Ashif.

18 * 16 = 288.

The product of HCF 18 and LCM 16 is?

Can anyone help to get the answer?

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 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.

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

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

LCM = Product of two numbers/HCF.

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