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

Thanks for Excellent explanation @Suraj.

@All.

Whenever we see highest, greatest, largest, etc -> this kind words in question, then take HCF.

And whenever we see smallest, lowest, etc -> this kind of words in question, then take LCM.

Thank you @Harish.

1305, 4665, 6905 -----> These are the numbers.

In this question why we subtract the numbers because here, it is said that they have the same remainder.

So, 1305 = hcf * x + remainder -----> (1),

4665 = hcf * y + remainder -----> (2),

6905 = hcf * z + remainder -----> (3),

Where x, y, z are respective quotients.
Now we take (2) - (1).
3360 =hcf (y-x) -----> (4),
From (3) - (2) we have
2240 = hcf (z - y) -----> (5),
From(3) - (1) we have
5600 = hcf (z - x) -----> (6),
Now we can see from the equation (4), (5), (6) hcf of the three numbers is the hcf of the three numbers. So the hcf of 6905, 4665 and 1305 = hcf of the three numbers 5600, 3360, 2240 = 1120.

Why should we subtract before finding out the HCF? can anybody tell me?

@Srinivas.

Thanks, this is the perfect explanation like a true mathematician.

Thanks for this complete explanation @M. Harish and @Srinivas.

Thanks for excellent explanation @Yogesh.

How (1 + 1 + 2 + 0)?

Please tell me.

Thanks @Saraswati.