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Question
Find the smallest square number divisible by each one of the numbers 8, 9 and 10.
Solution
Given: The least-square number which is exactly divisible by 8, 9 and 10 is equal to L.C.M. of 8, 9 and 10.
| 2 | 8, 9, 10 |
| 2 | 4, 9, 5 |
| 2 | 2, 9, 5 |
| 3 | 1, 9, 5 |
| 3 | 1, 3, 5 |
| 5 | 1, 1, 5 |
| 1, 1, 1 |
Hence, their L.C.M. is 2 × 2 × 2 × 3 × 3 × 5 = 360
As we see, (2 × 2) × 2 × (3 × 3) × 5
i.e. 2 and 5 is not able to make their pair.
Hence, to make it perfect square, it must be multiplied with 2 × 5 = 10
As, 360 × 10 = 3600
Hence, 3600 is least square number which is exactly divisible by 8, 9 and 10.
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