Question

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

Answer 1

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.

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