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Question
Find the least square number which is exactly divisible by 3, 4, 5, 6 and 8.
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Solution
The least square number divisible by each of 3, 4, 5, 6 and 8 is equal to the LCM of 3, 4, 5, 6 and 8.
| 2 | 3, 4, 5, 6, 8 |
| 2 | 3, 2, 5, 3, 4 |
| 2 | 3, 1, 5, 3, 2 |
| 3 | 3, 1, 5, 3, 1 |
| 5 | 1, 1, 5, 1, 1 |
| 1, 1, 1, 1, 1 |
∴ LCM of 3, 4, 5, 6 and 8 = 2 × 2 × 2 × 3 × 5 = 120
The prime factorisation of 120 = (2 × 2) × 2 × 3 × 5
Here, prime factors 2, 3 and 5 are unpaired.
Clearly, to make it a perfect square, it must be multiplied by 2 × 3 × 5, i.e. 30.
Therefore, required number = 120 × 30 = 3600
Hence, the least square number is 3600.
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