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Let x be the least number of 4 digits that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If x lies between 2000 and 2500, then what is the sum of the digits of x?

Let x be the least number of 4 digits that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If x lies between 2000 and 2500, then what is the sum of the digits of x? Correct Answer 4

LCM = 2 × 2 × 3 × 5 × 7 = 420

LCM of 2, 3, 4, 5, 6 and 7 is 420.

Number should be between 2000 and 2500 so, the number is = 420 × 5 = 2100

Remainder will be 1 in each case so the number is = 2100 + 1 = 2101

Sum of digit of the number 2101 is = 2 + 1 + 0 + 1 = 4

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