Question

12. What is the smallest perfect square which is exactly divisible by 9, 12, 15, and 20?​

Answer 1

Answer:

30 is the smallest perfect square

Answer 2

$\bf\red{\underline{\boxed{Question}}}$

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$\small\text{What is the smallest perfect square which is }\\{\small\text{exactly divisible by 9, 12, 15, and 20?}}$

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$\bf\red{\underline{\boxed{Solution}}}$

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✏$\small\text{To find a number which is divisible by }\\{\small\text{ 9 , 12 , 15 , and 20}}$

$\small\text{Lets find the LCM to these number}$

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3 | 9 12 15 20

3 | 3 4 5 20

4 | 1 4 5 20

5 | 1 1 5 5

$\:\:\:$ | 1 1 1 1

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$\small\tt{LCM\rightarrow\: 3 \times3\times4\times5 \:=\: 180 }$

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$\small\text{As 180 is not a perfect square }$

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$\small\text{we have to multiply it by 5 to make }\\{\small\text{it a perfect sqaure}}$

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$\small\tt{ we \:get\: 180 \: \times5\: =\: 900}$

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$\small\text{Hence 900 is the number which is}\\{\small\text{divisible by 9 , 12 , 15 , 18 }}$

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$\bf\red{\underline{\boxed{Thanks}}}$