Multiple choice

Find the least number which when divided by $20, 18$ and $30$ gives the same remainder $9$ in each case.

  1. $179$
  2. $189$
  3. $169$
  4. $199$
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B Correct answer
Explanation

The number must be of the form LCM(20, 18, 30) + 9. The LCM of 20, 18, and 30 is 180. Adding the remainder 9 gives 189.

AI explanation

The required number must exceed the least common multiple of the divisors by the value of the remainder. The prime factorization shows the least common multiple of 20, 18 and 30 is 180. Adding the given remainder of 9 to 180 gives 189.

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