Question

Question 131

Solve the following question:

Find the smallest square number divisible by each of the numbers 8, 9 and 10.

Answer 1

The least number divisible by each of the numbers 8, 9 and 10 is equal to the LCM of 8, 9 and 10
$\begin{array}{cc}2& 8,9,10\\ 2& 4,9,5\\ 2& 2,9,5\\ 3& 1,9,5\\ 3& 1,3,5\\ 5& 1,1,5\\ & 1,1,1\end{array}$
$\therefore$ LCM of 8, 9 and 10 $=2\times 2\times 2\times 3\times 3\times 5=360$
Prime factors of 360 $=(2\times 2)\times 2\times (3\times 3)\times 5$
Here, prime factors 2 and 5 are unpaired. Clearly, to make it a perfect square, it must be multiplied by $2\times 5$, ie. 10
Therefore, required number $=360\times 10=3600$
Hence, the smallest square number divisible by each of the numbers 8, 9 and 10 is 3600.