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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 = 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 10000/600, we get remainder as 400 Then, the answer = 1000 - (600 - 400) - 9 = 10191

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