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

Discussion Forum : Problems on H.C.F and L.C.M - General Questions (Q.No. 14)
14.
The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
1677
1683
2523
3363
Answer: Option
Explanation:

L.C.M. of 5, 6, 7, 8 = 840.

Required number is of the form 840k + 3

Least value of k for which (840k + 3) is divisible by 9 is k = 2.

Required number = (840 x 2 + 3) = 1683.

Discussion:
87 comments Page 5 of 9.

JITENDRA KUMAR said:   7 years ago
What is the Value of k?

SHANKAR said:   7 years ago
Simply we can solve this by;

1+6+8+3=18
1+6+7+7=21
Same as other;

18 is divided by 9 and then B is correct.

Neelima said:   7 years ago
@All.

Hai I have a doubt, everyone is explaining from 840k+3 but here the doubt is we got lcm 840 if 5 6 7 8 divide the 840 answer is 0.

So, 840 + 3=843 now we will get remainder 3 but here 5 is divisor 840 is dividend so how you come 840k+3? Explain it.

Bodla aravind said:   6 years ago
Let (840k + 3) = 1683 [ 1683 taken from Option B].
Therefore, k = (1683-3)/840.
k = 1680/840,
k= 2.

Shariq said:   1 decade ago
Just divide all options by 9.

Naveen said:   1 decade ago
840/9 =93 and leaves reminder 3.

Now 9*93 + (3 * x +3) now find the value of x in (3* x + 3) which is divisible by 9.

If you put 2 then it is divisible by 9 i.e., (3*2+3).

So k=2.

Lali said:   1 decade ago
It clear when we put a value of k 1 then 5,6,7,8, leave the remainder 3 and 6 in case of 9. when k=2. in this case no remainder is left.

Chandresh said:   1 decade ago
But concept of finding the value of k is still not clear.

Can anyone tell the concept except logical solution?

Satheesh said:   1 decade ago
Divide each answer by 9 which one has no reminder that's answer.

Feroz said:   1 decade ago
we get LCM =840 since 843 is divided by 3
when we divide it by 9 it leaves a remainder of 6
since we need a least no. divided by three which also leaves 3 remainder
we put value of k=1, 2, 3.... till we get the required no.
since


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