Multiple choice

What is the smallest number which leaves remainder 3 when divided by any of the numbers 5, 6 or 8 but leaves no reminder when it is divided by 9?

  1. 123

  2. 603

  3. 723

  4. 243
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Number leaves remainder 3 when divided by 5, 6, or 8, so it equals LCM(5,6,8)×k + 3 = 120k + 3. It must also be divisible by 9. Testing values: 123 (k=1) not divisible by 9; 243 (k=2) = 243, which is divisible by 9 (2+4+3=9). Verify: 243 ÷ 5 = 48 rem 3, 243 ÷ 6 = 40 rem 3, 243 ÷ 8 = 30 rem 3, 243 ÷ 9 = 27 rem 0.

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