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 2 of 9.
Kannan said:
1 decade ago
In the below eqn.
Least value of k for which (840k + 3) is divisible by 9.
K can be K=0,1,2...
Sub K=1,
(840*1)+3 =-- Not divisible by 9.
Sub K=2,
(840*2)+3 = 187-- Divisible by 9.
Sub K=3,
(840*3)+3 =-- Not Divisible by 9.
Hence take lease no. (i.e 2).
Least value of k for which (840k + 3) is divisible by 9.
K can be K=0,1,2...
Sub K=1,
(840*1)+3 =-- Not divisible by 9.
Sub K=2,
(840*2)+3 = 187-- Divisible by 9.
Sub K=3,
(840*3)+3 =-- Not Divisible by 9.
Hence take lease no. (i.e 2).
(1)
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.
Ayush said:
1 decade ago
To find value of k, see the following:
840k+3 = 0 (mod9).
30k+3 = 0 (mod9) [840/9=30 (mod9)].
30k = 6 (mod9).
3k = 6 (mod9) [30/9=3 (mod9)].
Dividing both sides by 3, we get
k = 2 (mod9).
So, the value of k = 2.
HOPE THIS ONE ALSO HELPED YOU.
840k+3 = 0 (mod9).
30k+3 = 0 (mod9) [840/9=30 (mod9)].
30k = 6 (mod9).
3k = 6 (mod9) [30/9=3 (mod9)].
Dividing both sides by 3, we get
k = 2 (mod9).
So, the value of k = 2.
HOPE THIS ONE ALSO HELPED YOU.
SURESH BINWAL said:
9 years ago
Any number whose digits sum is nine (9) then only the number is divisible by nine.
taking k = 1..means 843 , sum will be 8+4+3 = 15 not divisible by nine.
k = 2 is 1643 & sum of digit is 1+6+4+3 = 18 means 1+8 = 9 hence least number is k=2.
taking k = 1..means 843 , sum will be 8+4+3 = 15 not divisible by nine.
k = 2 is 1643 & sum of digit is 1+6+4+3 = 18 means 1+8 = 9 hence least number is k=2.
Samiul sk said:
9 years ago
Find the least number which when divided by 12, leaves a remainder of , when divided by 15, leaves a remainder of 10, when divided by 16, leaves a remainder of 11.
(a)115 (b)235 (c)247 (d)475
Solve and find the answer.
(a)115 (b)235 (c)247 (d)475
Solve and find the 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
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
Anand said:
1 decade ago
The solution of finding the option which is divisible by 9 works only in this specific case of provided options. In case, when more than 1 option is divisible by 9, the method to find out the value of k needs to be understood.
Munna Mudassir said:
8 years ago
Another shortcut which will work in this case is checking thew divisibility by 9.
only 1683 is divisible by 9 hence the answer is 1683. In case there is more numbers divisible by you have to check it as my previous answer.
only 1683 is divisible by 9 hence the answer is 1683. In case there is more numbers divisible by you have to check it as my previous answer.
Sandeep said:
8 years ago
Find the least number which when divided by 16,18,20,25 leaves 4 as a remainder in each case but when divided by 7 leaves no remainder.
a) 17004
b) 18000
c) 18002
d) 18004
Can anyone explain the answer?
a) 17004
b) 18000
c) 18002
d) 18004
Can anyone explain the answer?
Uttam said:
1 decade ago
Just try this,
Sum the digits of each option given. i.e
[A].1+6+7+7=21 [B].1+6+8+3=18
[C].2+5+2+3=12 [D].3+3+6+3=15
Now only 18 is divisible by 9
So answer should be 1683 that is option B.
Sum the digits of each option given. i.e
[A].1+6+7+7=21 [B].1+6+8+3=18
[C].2+5+2+3=12 [D].3+3+6+3=15
Now only 18 is divisible by 9
So answer should be 1683 that is option B.
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