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Question
Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.
Solution
LCM of 8, 10 and 12
| 2 | 8, 10, 12 |
| 2 | 4, 5, 6 |
| 2 | 2, 5, 3 |
| 3 | 1, 5, 3 |
| 5 | 1, 5, 1 |
| 1, 1, 1 |
LCM = 2 × 2 × 2 × 3 × 5 = 120
We have to find the greatest 3-digit multiple of 120.
It can be seen that 120 × 8 = 960 and 120 × 9 = 1080.
Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.
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