question_answer 20)

                Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

Answer:

                The least number divisible by each one of 4, 9 and 10 is their L.C.M.

2	4, 9, 10
2	2, 9, 5
3	1, 9, 5
3	1, 3, 5
5	1, 1, 5
	1, 1, 1

The L.C.M. of 4, 9 and 10 is \[2\times 2\times 3\times 3\times 5=180\]. Now prime factorisation of 180 is \[180=\underline{2\times 2}\times \underline{3\times 3}\times 5\]. The prime factor 5 is not in pair Therefore 180 is not a perfect square.     In order to get a perfect square, caw factor of 180 must be paired. So we need to make pair of 5.                          Therefore 180 should be multiplier by 5.                                    Hence, the required smallest square number is \[180\times 5=900\].