Multiple choice

Find the least number of five digits which when divided by $16, 24, 30$ and $32$ leaves a remainder $2$ in each case.

  1. $10084$
  2. $10071$
  3. $10082$
  4. $10002$
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C Correct answer
Explanation

The LCM of 16, 24, 30, 32 is 480. The smallest 5-digit number is 10000. 10000 / 480 = 20.83. 480 * 21 = 10080. Adding the remainder 2 gives 10082.

AI explanation

First find the least common multiple of 16, 24, 30, and 32, which is 480. The least five-digit number is 10000. Divide 10000 by 480 to get a quotient of 20 and a remainder of 400. The next multiple of 480 is 480 times 21, which equals 10080. Because the required remainder is 2, add 2 to 10080 to get 10082.

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