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

Why are we adding 8 with the lcm I don't get that because in some cases we do subtract the remainder from the lcm so could someone please help me out with this?

How?

Anybody can explain ?

@unknown.

Given nor.s in increasing order:12,15,20,54
At the beginning take first two numbers are;

Then do division operation i.e
12)15(1
12
________
03)12(4
12
_________
0(remainder )

If remainder becomes 0,then take divisor of last operation, i.e 3
Now division operation b/ w 3 and 20
3)20(6
18
____
2)3(1
2
______
1)2(2
2
____
0

Similarly now proceed with 1 n 54
1)54(54
54
___
0
.: last divisor 1 is the required H.C.F.

Can anyone please show me the procedure to calculate the lcm as I think I am making some mistake.

First divide entire given series with 2 then you have the remainders 6, 15, 10, 27.

Now divide these series with 3 then you get reminders 2, 5, 10, 9.

Now divide before series with 5 then you will get series 2, 1, 2, 9.

Now divide before series with 2 then you will get series 1, 1, 1, 9.

Now multliply all the divisors that used in it i.e 2*3*5*2*9 = 540.

Please tell me how to find the HCF of 15, 12, 20, 54.

Yes @Jalpan even I am confused as to when you need to subtract and when you need to add the remainder. Can anyone explain?

Shouldn't the answer be 8 here?

Please anyone tell me what is the least natural number which when divided by 2, 3, 4, 5 or 6 leaves a remainder 1.

L.C.M
2 | 12,15,20,54
2 | 6 ,15,10,27
3 | 3 ,15,5 ,27
5 | 1 ,5 ,5 ,9
1 ,1 ,1 ,9
NOW,2*2*3*5*9=540
Required number = (L.C.M. of 12, 15, 20, 54) + 8

= 540 + 8

= 548.