Answer:
The least number divisible by each one of 8, 15 and 20 is their L.C.M.
The L.C.M. of 8, 15 and 20 is \[2\times 2\times 2\times 3\times 5=120\] Now prime factorisation of 120 is \[120=\underline{2\times 2}\times 2\times 3\times 5\] The prime factors 2, 3 and 5 are not in pairs. Therefore, 120 is not a perfect square. In order to get a perfect square, each factor of 120 must be paired. So, we need to make pairs of 2, 3 and 5. Therefore 120 should be multiplied by \[2\times 3\times 5\]; i.e. 30. Hence, the required smallest square number is \[120\ \times 30=3600\]. 2 8, 15, 20 2 4, 15, 10 2 2, 15, 5 3 1, 15, 5 5 1, 5, 5 1, 1, 1
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