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

Agree @Sanidhya.

Can anyone explain us?

Why isn't the answer 3/5 as 3/5 divides all numbers and it is also higher than 3/1400?

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.

Thats long process, tell me short cut method.

Why we have taken LCM of denominator?

Can you please explain shortcut?

What is the need for so much of calculations?

Since we know that HCF of any fraction is computed with the following formula = HCF of Numerators/LCM of denominators.

Now see the Options:

Numerators has to be less than the given numbers (9, 12, 18, 21) since, it is HCF. This rules out Options B and D. We are left with options A and C.

Now denominator is the LCM which shall be more than the given number i.e. 10, 25, 35, 40. Therefore Options C is the correct answer.