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प्रश्न
Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.
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उत्तर
The number that will be perfectly divisible by each one of 4, 9, and 10 is their LCM. The LCM of these numbers is as follows:
| 2 | 4, 9, 10 |
| 2 | 2, 9, 5 |
| 3 | 1, 9, 5 |
| 3 | 1, 3, 5 |
| 5 | 1, 1, 5 |
| 1, 1, 1 |
LCM of 4, 9, 10 = 2 × 2 × 3 × 3 × 5 = 180
Here, prime factor 5 does not have its pair. Therefore, 180 is not a perfect square. If we multiply 180 with 5, then the number will become a perfect square. Therefore, 180 should be multiplied with 5 to obtain a perfect square.
Hence, the required square number is 180 × 5 = 900.
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