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Question
Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.
Solution
The number that is perfectly divisible by each of the numbers 8, 15, and 20 is their LCM.
| 2 | 8, 15, 20 |
| 2 | 4, 15, 10 |
| 2 | 2, 15, 5 |
| 3 | 1, 15, 5 |
| 5 | 1, 5, 5 |
| 1, 1, 1 |
LCM of 8, 15, and 20 = 2 × 2 × 2 × 3 × 5 = 120
Here, prime factors 2, 3, and 5 do not have their respective pairs. Therefore, 120 is not a perfect square.
Therefore, 120 should be multiplied by 2 × 3 × 5, i.e., 30, to obtain a perfect square.
Hence, the required square number is 120 × 2 × 3 × 5 = 3600
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