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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:
- a)1677
- b)1683
- c)2523
- d)3363
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The least number which when divided by 5, 6 , 7 and 8 leaves a remaind...
LCM of 5, 6, 7 and 8 = 840.
Hence the number can be written in the form (840k + 3) which is divisible by 9.
If k = 1, number = (840 x 1) + 3 = 843 which is not divisible by 9.
If k = 2, number = (840 x 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.
Most Upvoted Answer
The least number which when divided by 5, 6 , 7 and 8 leaves a remaind...
Concept: LCM method
Explanation:
To find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, we can use the LCM method.
Step 1: Find the LCM of 5, 6, 7 and 8.
5 = 5 x 1
6 = 2 x 3
7 = 7 x 1
8 = 2 x 2 x 2
LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840
Step 2: Subtract 3 from the LCM obtained in step 1.
840 - 3 = 837
Step 3: Check if the number obtained in step 2 is divisible by 9.
Sum of digits of 837 = 18
Since 18 is divisible by 9, 837 is also divisible by 9.
Therefore, the required number is 837.
Answer:
Option B - 1683.
Explanation:
To find the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, we can use the LCM method.
Step 1: Find the LCM of 5, 6, 7 and 8.
5 = 5 x 1
6 = 2 x 3
7 = 7 x 1
8 = 2 x 2 x 2
LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840
Step 2: Subtract 3 from the LCM obtained in step 1.
840 - 3 = 837
Step 3: Check if the number obtained in step 2 is divisible by 9.
Sum of digits of 837 = 18
Since 18 is divisible by 9, 837 is also divisible by 9.
Therefore, the required number is 837.
Answer:
Option B - 1683.
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