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Answer :
We have, LCM of 4, 9, 10 = 180
\(\qquad \begin{array}{c|lcr}
2 & 4 \;,\;9\;,\;10\\
\hline
2 & 2 \;,\;9\;,\;5\\
\hline
3 & 1 \;,\;9\;,\;5\\
\hline
3 & 1 \;,\;3\;,\;5\\
\hline
5 & 1 \;,\;1\;,\;5\\
\hline
& 1\;,\;1\;,\;1\\
\end{array}
\)
The least number divisible by 4, 9 and 10 = 180
Now we have, prime factors of 180 as:
\(180 = 2 \times 2 \times 3 \times 3 \times 5\)
Here, 5 has no pair.So the smallest number to be multiplied to make it a perfect square is 5.
The required smallest square number = \(180 \times 5 = 900\)