Multiple choice

Find the least five digit number, which when divided by 12, 18, 21 and 28, leaves the same remainder.

  1. $11019$
  2. $10081$
  3. $10059$
  4. $10289$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

LCM(12,18,21,28) = 252. If N leaves remainder r when divided by each, then N-r must be divisible by LCM. So N = 252k + r. We need the smallest 5-digit N. Checking: 10081 = 252×40 + 1, which gives remainder 1 when divided by 12, 18, 21, and 28. 10059 also works but is smaller.

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