Multiple choice

Find the lowest number which when divided by 8, 12, 15 and 20 leaves the remainder 2.

  1. 360

  2. 242

  3. 122

  4. 82
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Find LCM of 8, 12, 15, 20 = 120. The required number must be 2 more than a multiple of 120. Check options: 360 ÷ 120 = 3, so 360 + 2 = 362 (not in options). 242 = 2 × 120 + 2 = 242 ✓. Wait, let me recalculate: LCM(8,12,15,20) = 120. We need a number N such that N ≡ 2 (mod 8), N ≡ 2 (mod 12), N ≡ 2 (mod 15), N ≡ 2 (mod 20). This means N-2 must be divisible by LCM = 120. So N = 120k + 2. For k=1: N=122. 122 ÷ 8 = 15R2, 122 ÷ 12 = 10R2, 122 ÷ 15 = 8R2, 122 ÷ 20 = 6R2. Yes, 122 is correct.

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