Find the least square number which is exactly divisible by $3, 4, 5, 6$ and $8.$
✓
Answer
The least square numbers divisible by each of $3, 4, 5, 6$ and $8$, is equal to the
LCM of $3, 4, 5, 6$ and $8$.
$\begin{array}{c|c}2 & 3,4,5,6,8 \\ \hline2 & 3,2,5,3,4\\\hline2&3,1,5,3,2\\\hline3&3,1,5,3,1\\\hline5&1,1,5,1,1\end{array}$
$\therefore LCM$ of $3, 4, 5, 6$ and $8 = 2 \times 2 \times 2 \times 3 \times 5 = 120$
The prime factorisation of $120 = (2 \times 2) \times 2 \times 3 \times 5$
Here, prime factors $2, 3$ and $5$ are unpaire Clearly, to make it a perfect square, it must be multiplied by $2 \times 3 \times 5$
, i.e. $30$. Therefore, required number $= 120 \times 30 = 3600$
Hence, the least square number is $3600$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.