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