Question

Question 10
Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

Answer 1

$\begin{array}{cc}2& 8-15-120\\ 2& 4-15-60\\ 2& 2-15-30\\ 3& 1-15-15\\ 5& 1-5-5\\ & 1-1-1\end{array}$

$\Rightarrow 2\times 2\times 2\times 3\times 5=120$
L.C.M. of 8, 15 and 20 is 120.

Here, prime factor 2, 3 and 5 has no pair.
Therefore 120 must be multiplied by $2\times 3\times 5$ to make it a perfect square.
$\Rightarrow 120\times 2\times 3\times 5=3600$

Hence,the smallest square number which is divisible by 8, 15 and 20 is 3600.