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Question
Find the smallest square number that is divisible by each of the numbers 8, 15, and 20.
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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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