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:
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 4 of 9.
Renu said:
8 years ago
Good explanation, Thanks @Suchita.
Ram said:
8 years ago
Thanks for the explanation @Suchita.
Tg said:
8 years ago
2 has come because 5*6*7*8 is 1683.
Shruthi Aishwarya said:
8 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.
Gowtham said:
8 years ago
Well said, thanks @Suchita.
Sudip said:
8 years ago
Thanks for the answer @Suchita.
Anjali said:
8 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.
Option B.
1+6+8+3=18 which is divisible by 9.
While other options are not divisible by 9.
Kannan said:
7 years ago
How k= 2? Explain.
Prekaha Darshan said:
7 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.
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.
Shwetha said:
7 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.
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.
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