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 3 of 9.
Gogol said:
1 decade ago
@SUCHITA
If one of the option becomes for example..2538, then the sum of 2+5+3+8= 18 will also be divided by 9 leaving no remainder.
So, in this case there is no profit from your logic.
If one of the option becomes for example..2538, then the sum of 2+5+3+8= 18 will also be divided by 9 leaving no remainder.
So, in this case there is no profit from your logic.
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.
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.
Sundar said:
1 decade ago
Let (840k + 3) = 1683 [ 1683 taken from Option B]
Therefore, k = (1683-3)/840
k = 1680/840
k = 2.
Note: (840k + 3) should be divisible by 9 if we substitute k = 2.
Therefore, k = (1683-3)/840
k = 1680/840
k = 2.
Note: (840k + 3) should be divisible by 9 if we substitute k = 2.
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.
SHIVA SHANKAR said:
8 years ago
Please clarifly my doubt after find out LCM for the numbers 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3.
How K = 2 comes please clarify friends.
Required number is of the form 840k + 3.
How K = 2 comes please clarify friends.
Lavi said:
1 decade ago
Oh, its simple one. You have to check only options. As question said when divided by 9 leaves no remainder. Means you have to check the divisibility of 9.
ABILASH said:
2 months ago
@All.
It's that simple.
Just check the numbers using the divisibility rule of 9.
It's nothing, but the sum of the numbers should be divisible by 9.
It's that simple.
Just check the numbers using the divisibility rule of 9.
It's nothing, but the sum of the numbers should be divisible by 9.
(5)
Tina Bhattacharjee said:
9 years ago
@Suchita.
18 is divisible by 6. There is no remainder. But as per the question, we should get 3 as the remainder when we divide the number by 6.
18 is divisible by 6. There is no remainder. But as per the question, we should get 3 as the remainder when we divide the number by 6.
Suchita said:
1 decade ago
hey.....just add the digits of given options as
1+6+8+3=18 the answer is that which can be divided by 9.
remaining numbers can't divide by 9.
1+6+8+3=18 the answer is that which can be divided by 9.
remaining numbers can't divide by 9.
Bhagirath said:
8 years ago
Lcm of 5,6,7, and8=840.
840÷9=93,leaves remainder =3.
multiply all the values=5*6*7*8=1680.
and leaves remainder are added =1680+3=1683.
840÷9=93,leaves remainder =3.
multiply all the values=5*6*7*8=1680.
and leaves remainder are added =1680+3=1683.
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