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Question
Find the smallest square number that is divisible by each of the numbers 4, 9, and 10.
Solution
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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