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

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Solution

L.C.M. of 4, 9 and 10 is 180. Prime factors of $180 = 2 \times 2 \times 3 \times 3 \times 5$ Here, prime factor 5 has no pair. Therefore, 180 must be multiplied by 5 to make it a perfect square.

$180 \times 5 = 900$ Hence, the smallest square number which is divisible by 4, 9 and 10 is 900.

$\begin{matrix} 2 & 180 2 & 90 3 & 45 3 & 15 5 & 5 1 \end{matrix}$

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