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:
86 comments Page 8 of 9.
Kannan said:
6 years ago
How k= 2? Explain.
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.
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:
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.
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.
JITENDRA KUMAR said:
6 years ago
What is the Value of k?
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.
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:
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.
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.
Therefore, k = (1683-3)/840.
k = 1680/840,
k= 2.
Amendra said:
6 years ago
How does the value of k equals 2?
Nancy said:
6 years ago
I can't understand how k=2? Explain.
(2)
Ramya namani said:
5 years ago
Or simply you can go for option verification.
Check the options whether it is divisible by 9.
Only 1683 is divisible by 9.
Check the options whether it is divisible by 9.
Only 1683 is divisible by 9.
(2)
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