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

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

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

Dividend = Divisor * Quotient + Remainder.

That's why +8.

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.

@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.

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?

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?

Can anyone tell me what is the smallest number which when divided by 12, 20, 36 leaves no remainder?

Please answer it.

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.

@Fia.

The LCMof the number is 48 .plus add remainder 7 = 55.
Answer is 55.