Multiple choice

Find the smallest number which when divided by 5, 6, 8 and 9 gives remainder 3 in each case.

  1. $360$
  2. $420$
  3. $363$
  4. $423$
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C Correct answer
Explanation

We need a number that when divided by 5, 6, 8, 9 gives remainder 3. This means if we subtract 3 from the number, it must be divisible by all four numbers. Find LCM(5,6,8,9). Prime factors: 5, 2×3, 2^3, 3^2. LCM = 5 × 2^3 × 3^2 = 5 × 8 × 9 = 360. The smallest such number is 360+3=363. Checking: 363÷5=72 rem 3, 363÷6=60 rem 3, 363÷8=45 rem 3, 363÷9=40 rem 3.

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