Find the smallest perfect square number that is divisible by 16, 24, and 36.

Question

14-07-2024
Mathematics

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Find the smallest perfect square number that is divisible by 16, 24, and 36.

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-07-14T15:15:31-04:00

To find the smallest perfect square number that is divisible by 16, 24, and 36, we will follow these steps:

1. Find the Least Common Multiple (LCM) of 16, 24, and 36:

- First, determine the LCM of 16 and 24.
- Next, use this result to find the LCM of that result with 36.

The LCM of 16 and 24 is 48.
The LCM of 48 and 36 is 144.

Therefore, the LCM of 16, 24, and 36 is 144.

2. Find the smallest perfect square greater than or equal to the LCM:

- We need to find the smallest perfect square that is greater than or equal to 144.
- The square root of 144 is 12, and squaring it gives us [tex]$ 12^2 = 144 $[/tex].

Since 144 is a perfect square and it is divisible by 16, 24, and 36, it qualifies as our answer.

Therefore, the smallest perfect square number which is divisible by 16, 24, and 36 is 144.