question_answer 1)

                Find the smallest square number that is divisible by each of the numbers 8, is and 20,                               

Answer:

                The least number divisible by each one of 8, 15 and 20 is their L.C.M.

2	8, 15, 20
2	4, 15, 10
2	2, 15, 5
3	1, 15, 5
5	1, 5, 5
	1, 1, 1

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 \[120\ \times 30=3600\].