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Question
Determine the smallest 3-digit number which is exactly divisible by 6, 8, and 12.
Solution
Smallest number = LCM of 6, 8, 12
| 2 | 6, 8, 12 |
| 2 | 3, 4, 6 |
| 2 | 3, 2, 3 |
| 3 | 3, 1, 3 |
| 1, 1, 1 |
LCM = 2 × 2 × 2 × 3 = 24
We have to find the smallest 3-digit multiple of 24.
It can be seen that 24 × 4 = 96 and 24 × 5 = 120.
Hence, the smallest 3-digit number which is exactly divisible by 6, 8, and 12 is 120.
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