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:
86 comments Page 2 of 9.

Neelima said:   6 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.

SHANKAR said:   6 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.

JITENDRA KUMAR said:   6 years ago
What is the Value of k?

Shwetha said:   6 years ago
@Aall.

The solution is;
Check :A-1677 divisible given no 5 we get reminder 2 so this not correct.

Then next B-1683 divisible given no 5 we will get reminder 3 next.
Divisible no 6 we get reminder 3.
Divisible 7 and 8 also we get reminder 3.
Then; 1+6+8+3=18, divisible by 9 so answer is B correct.

Prekaha Darshan said:   6 years ago
In simple when we go with options

Option A)1677
1677/9, remainder=3.

Option B) 1683
1683/9, remainder=0.

Option C) 2523
2523/9, remainder=3.

Option D) 3363
3363/9, remainder=3.

When 1683/5, 1683/6, 1683/7, 1683/8 leaves the remainder of 3 and 1683/9 leaves no remainder.

Hence, the correct option is B.

Kannan said:   6 years ago
How k= 2? Explain.

Anjali said:   7 years ago
Check the 4 options divisibility for 9.

Option B.
1+6+8+3=18 which is divisible by 9.
While other options are not divisible by 9.

Sudip said:   7 years ago
Thanks for the answer @Suchita.

Gowtham said:   7 years ago
Well said, thanks @Suchita.

Shruthi Aishwarya said:   7 years ago
Apply the divisibility test of 9 to the options, in this case only 1683 and 3363 are divisible by 9. Since they have asked for the least number 1683 is the answer.


Post your comments here:

Your comments will be displayed after verification.