Multiple choice

What is the least possible number which when divided by 2,3,4,5,6 it leaves the remainder 1, 2,3,4,5?

  1. $104$
  2. $205$
  3. $59$
  4. $87$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We need N such that N ≡ 1 (mod 2), N ≡ 2 (mod 3), N ≡ 3 (mod 4), N ≡ 4 (mod 5), N ≡ 5 (mod 6). Notice each remainder is one less than the divisor. This means N + 1 is divisible by 2, 3, 4, 5, and 6. So N + 1 = LCM(2,3,4,5,6) × k = 60k. Therefore N = 60k - 1. For k = 1, N = 59. Checking: 59 ÷ 2 = 29 R1 ✓, 59 ÷ 3 = 19 R2 ✓, 59 ÷ 4 = 14 R3 ✓, 59 ÷ 5 = 11 R4 ✓, 59 ÷ 6 = 9 R5 ✓.

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