What is the least number which when divided by 5 6 7 8 gives reminder 3 in each case and is completely divisible by 9?

Answer: Option A

Explanation:

Solution 1LCM of 5, 6, 7 and 8 = 840Hence the number can be written in the form (840k + 3) which is divisible by 9.If k = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9.If k = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9.

Hence 1683 is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.

Solution 2 - Hit and Trial MethodJust see which of the given choices satisfy the given condtions.Take 3363. This is not even divisible by 9. Hence this is not the answer.Take 1108. This is not even divisible by 9. Hence this is not the answer.Take 2007. This is divisible by 9.2007 ÷ 5 = 401, remainder = 2 . Hence this is not the answerTake 1683. This is divisible by 9.1683 ÷ 5 = 336, remainder = 31683 ÷ 6 = 280, remainder = 31683 ÷ 7 = 240, remainder = 31683 ÷ 8 = 210, remainder = 3

Hence 1683 is the answer

Sum of digits in the numbers must be multiples of 9 

so of all we have 2 options left

B and C

in these when1683 divisible by 5 remainder is 3 check that

answer is 

I cant understand y u hav added 3 with 840?

(use Q&A for new questions)

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What is the least number which, when divided by 5,6,7 and 8 gives the remainder 3 but is divisible by 9 ?

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Given:

The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3

The least number when divided by 9 remainder = 0

Concept Used:

For the least number take LCM and also check that all conditions are satisfying or not

For same remainder in each case add the remainder in the LCM 

Calculation:

First we have to find the LCM of 5, 6, 7, 8

5 = 51

6 = 21 × 31 

7 = 71 

8 = 23 

LCM of 5, 6, 7, 8 is 23 × 31 × 51 × 71 = 840

For same remainder we have to add 3 to the LCM

⇒ 840 + 3 

Now check weather it is divisible by 9 or not

843/9 = Not divisible by 9

Now we have to take next multiple of LCM and then add 3

840 × 2 + 3

⇒ 1683

Divide it by 9

1683/9 = 187

⇒ 1683 is divisible by 9 

⇒ 1683 is the least number when divided by 5, 6, 7, 8 gives remainder 3

The least number must be divisible by 9 

For divisibility of 9 sum of digits of the number must be divisible by 9 

Checking it by options:

Option 1) 1677

1 + 6 + 7 + 7 = 21

⇒ 1677 is not divisible by 9

Option 2) 1683

1 + 6 + 8 + 3 = 18

⇒ 1683 is divisible by 9

Option 3) 2523

2 + 5 + 2 + 3 = 12

⇒ 2523 is not divisible by 9

Option 4) 3363

3 + 3 + 6 + 3 = 15

⇒ 3363 is not divisible by 9

∴ The least number is 1683 which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder.