Determine the greatest 3-digit number exactly divisible by 8, 10 and 12. and 6 ,8 and 10

Explanation

To determine the greatest 3-digit number exactly divisible by 8, 10, and 12, and also by 6, 8, and 10, we will follow these steps:

### Step 1: Find the LCM of 8, 10, and 12

1. **Prime Factorization**:
- 8 = 2 × 2 × 2 = \(2^3\)
- 10 = 2 × 5 = \(2^1 \times 5^1\)
- 12 = 2 × 2 × 3 = \(2^2 \times 3^1\)
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