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Question
Find the smallest 4-digit number which is divisible by 18, 24 and 32.
Solution
LCM of 18, 24 and 32
| 2 | 18, 24, 32 |
| 2 | 9, 12, 16 |
| 2 | 9, 6, 8 |
| 2 | 9, 3, 4 |
| 2 | 9, 3, 2 |
| 3 | 9, 3, 1 |
| 3 | 3, 1, 1 |
| 1, 1, 1 |
LCM = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
We have to find the smallest 4-digit multiple of 288.
It can be observed that 288 × 3 = 864 and 288 × 4 = 1152.
Therefore, the smallest 4-digit number which is divisible by 18, 24 and 32 is 1152.
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