Question

Find the least number which is a perfect square exactly divisible by 16, 24 and 32.

Answer 1

Step-by-step explanation:

$Let \: \: us \: \: find \: \: the \: \: LCM \: \: of \: \: 16, \: 24, \: 32 \\ 16 \: ➺ \: 2 \times 2 \times 2 \times 2 \\ 24 \: ➺ \: 2 \times 2 \times 2 \times 3 \\ 32 \: ➺ \: 2 \times 2 \times 2 \times 2 \times 2 \\ \\ LCM \: \: of \: \: 16, \: \: 24, \: \: 32 \\➺ \: 2 × 2× 2 × 2 × 2 × 3 \\ \\ Least \: \: Perfect \: \: Square \: \: can \: \: be : \\ ➺ \: {2}^{4} \times {2}^{2} \times {3}^{2} \\ ➺ \: 16 \times 4 \times 9 \\ ➺ \: \large{ \bf{576}}$