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 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.
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.
Lali said:
1 decade ago
It clear when we put a value of k 1 then 5,6,7,8, leave the remainder 3 and 6 in case of 9. when k=2. in this case no remainder is left.
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers