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

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 = $$180 \times 5 = 900$$