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

The Lcm is 3/2800.

For the same question instead of hcf if LCM was asked what will be the answer? Please solve it.

If we take LCM collectively, the HCF is 2 and 3, if one by one it's 3. How can we recognise that the HCF should be taken separately?

Answer Should be 3/2800.

Because,
H.C.F of 9, 12, 18, 21 is 3.
L.C.M of 10, 25, 35, 40 is 2800.

So, the answer is 3/2800.

Simply

Here HCF of 9 =3 * 3, 12 = 3 * 2 * 2, 18 = 3 * 3 * 2, and 21 = 3 * 7.
HCF = 3.

LCM of 10 =2 * 5, 25 = 5* 5, 35 = 3 * 7, 40 = 2* 2 * 2 * 5.
LCM = 1400.

Required HCF = HCF/LCM.
= 3/1400.

Actually, the answer is showing 3/2800. That's why getting confused. I also got the result 3/1400.

Is this the correct answer?

Why we have taken LCM of denominator?

Can you please explain shortcut?

The concept behind hcf/lcm is that suppose we take 9/10 now there should be a fraction a/b that exactly divides it (9/10) / (a/b) = (9*b) / (10*a) now you take a as hcf of all numbers (numerators only) that will exactly divide 9.

Now for b if you take hcf of denominators it will exactly divide 10 but now there will be a number in denominator of our expression giving us fraction but if we rather take lcm then 10 will go in integral number to divide b and we will get integer.