Find the least number of five digits which when divided by 40, 60, and 75, leave remainders 31, 51 and 66 respectively.

  • 110196
  • 210199
  • 310191
  • 410197
Answer:- 1
Explanation:-

Solution:
Difference, 40 - 31 = 9
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = {(LCM of 40, 60, 75)-9}

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600
But, the least number of 5 digits = 10000
10000600,
  we get remainder as 400
Then, the answer = 1000 - (600 - 400) - 9 = 10191

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  we get remainder as 400
Then, the answer = 1000 - (600 - 400) - 9 = 10191 ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "
Solution:
Difference, 40 - 31 = 9
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = {(LCM of 40, 60, 75)-9}

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600
But, the least number of 5 digits = 10000
10000600,
  we get remainder as 400
Then, the answer = 1000 - (600 - 400) - 9 = 10191 ", "dateCreated": "7/24/2019 10:09:12 AM" } }
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