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:
1677
1683
2523
3363
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.

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.

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.

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.

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.

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.

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.

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.


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