Question
Find the least square number which is divisible by $3,4,5,6$ and $8.$
✓
Answer
Firstly, we find out the LCM of $3, 4, 5, 6, 8$
To make $3 \times 2 \times 2 \times 2 \times 5$ a perfect square, we need to multiply it with $3 \times 2 \times 5$.
Thus, we have
$3 \times 2 \times 2 \times 2 \times 5 \times 3 \times 2 \times 5=120 \times 30=3600$
| 3 | 3, 4, 5, 6, 8 |
| 2 | 1, 4, 5, 2, 8 |
| 2 | 1, 2, 5, 1, 4 |
| 2 | 1, 1, 5, 1, 2 |
| 5 | 1, 1, 5, 1, 1 |
| 1, 1, 1, 1, 1 |
Thus, we have
$3 \times 2 \times 2 \times 2 \times 5 \times 3 \times 2 \times 5=120 \times 30=3600$
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