Question

The least square number which is exactly divisible by each of these number $6,9,15$ and $20$ is

• A. $1000$
• B. $900$
• C. $450$
• D. $180$

Answer 1

The correct option is B $900$

Smallest/ least number divisible by $6,9,15$ and $20$ is it's LCM
i.e.
LCM$=2\times 2\times 3\times 3\times 5=180$
On resolving 180 into prime factors $180.$
$=2\times 2\times 3\times 3\times 5$
Therefore, there is no factor to form pair of $5$ so to make it a perfect square so we multiply $180$ with $5$ to get $900.$
Hence least square number divisible by $6,9,15$ and $20$ is $900.$