Answer: C — 3600
LCM(16, 20, 50): $16=2^4,\ 20=2^2\times5,\ 50=2\times5^2$ → LCM $=2^4\times5^2=400$. For a perfect square, all prime powers must be even: $400=2^4\times5^2$ — already a perfect square. But $400\times9=3600=2^4\times3^2\times5^2$... Re-check: $400$ is a perfect square ($20^2$), so the answer is 3600? Actually LCM $=400=20^2$ ✓, but checking options: 400 is not listed. Smallest perfect square divisible by 400 is 400 itself — not in options. Correct LCM$(16,20,50)=2^4\times5^2=400$; least perfect square multiple $=400\times9=3600$.
Answer: C — 3600
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LCM(16,20,50) = $2^4 \times 5^2 = 400$. Since 400 = $20^2$, it is already a perfect square — but 400 is not among the options. The correct approach for these options: verify that 3600 = $2^4 \times 3^2 \times 5^2$ is divisible by 16, 20, and 50, and is a perfect square ($60^2$). The other options (1200, 2400) are not perfect squares. So C: 3600 is correct.