Question

Find the least perfect square which is exactly divisible by each of the numbers 6, 9, 15 and 20. [4 MARKS]

Answer 1

Concept : 1 Mark
Prime factorisation : 1 Mark
Conclusion : 2 Marks


The least number divisible by each of the numbers 6, 9, 15 and 20 is their LCM, which is

$(2\times 2\times 3\times 3\times 5)$

i.e., 180.

$180=2\times 2\times 3\times 3\times 5$

$\Rightarrow$ 180 is not a perfect square

To make it a perfect square, it must be multiplied by 5

$\therefore$ The required number $=180\times 5=900$