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

@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.

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.

Can any one tell me. Why + ?

Why - not ?

Because I have seen some examples where, if HCF then taking remainder plus with dividend and if LCM then taking remainder substracted from the dividend. Explain please.

2|12 15 20 54.
2|06 15 10 27.
3|03 15 05 27.
5|01 05 05 09.
9|01 01 01 09.
|01 01 01 01.

Best to find LCM solve till all value get 1.

You will always get perfect answer without confusion.

2*2*3*5*9 = 540.

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.

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?

Divide the series by 3 I get 4 5 20 18.

Further divide by a 4, 1 5 5 18. Again divide by 5 I end up with 1 1 1 18 now I get lcm = 1080. Am I right?

L.C.M
2 | 2,3,4,5,6
2 | 1,3,2,5,3,
3 | 1,3,1,5,3
| 1,1,1,5,1

NOW,2*2*3*5=60
Required number = (L.C.M. of 2, 3, 4, 5 and 6) + 1

= 60 + 1

= 61

LCM of 12, 15, 20, 24 is 540. Required no is 548. 548 is divided by 12, 15, 20, 24 respectively. The remainder is 8. That is the reason add 8.

What if it is to find the least number which when divided by 8, 12, 16 leaves remainder 7 in each case?

Please, anyone, tell me.