÷ 12 ≈ 8.33 → next integer is 9 → \(12 \times 9 = 108\)
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- A 3-digit number ranges from 100 to 999. A number divisible by 12 must be divisible by both 3 and 4.
- Find the smallest and largest 3-digit numbers divisible by 12:
- Smallest: Check divisibility:
- Largest: 999 ÷ 12 ≈ 83.25 → largest integer is 83 → \(12 \times 83 = 996\)
- These form an arithmetic sequence: \(108, 120, \dots, 996\) with \(a = 108\), \(l = 996\), \(d = 12\).
- l = a + (n-1)d \implies 996 = 108 + (n-1) \cdot 12
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