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

Find the least number of five digits which when divided by 40, 60, and 75, leave remainders 31, 51 and 66 respectively. Correct Answer 10191

Difference, 40 - 31 = 960 - 51 = 975 - 66 = 9Difference between numbers and remainder is same in each case.Then,The answer = {(LCM of 40, 60, 75) - 9}40 = 2 × 2 × 2 × 560 = 2 × 2 × 3 × 575 = 3 × 5 × 5LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600But, the least number of 5 digits = 10000$$\frac{{10000}}{{600}},$$   we get remainder as 400Then, the answer = 1000 - (600 - 400) - 9 = 10191

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