Find the lowest perfect squared number that is divisible by 12, 16, 20 and 24

Answer 1

To find the lowest perfect squared number that is divisible by 12, 16, 20, and 24, we need to find the least common multiple (LCM) of these numbers and then find the smallest perfect square greater than or equal to the LCM.

First, let's find the LCM of 12, 16, 20, and 24.

Prime factorization of 12: 2^2 * 3
Prime factorization of 16: 2^4
Prime factorization of 20: 2^2 * 5
Prime factorization of 24: 2^3 * 3

To find the LCM, we take the highest power of each prime factor that occurs in any of the numbers:

Highest power of 2: 2^4
Highest power of 3: 3
Highest power of 5: 5

Therefore, the LCM of 12, 16, 20, and 24 is 2^4 * 3 * 5 = 240.

The smallest perfect square greater than or equal to 240 is 15^2 = 225, which is NOT divisible by 12, 16, 20, or 24.

The next perfect square is 16^2 = 256, which is divisible by 12, 16, 20, and 24.

Therefore, the lowest perfect squared number that is divisible by 12, 16, 20, and 24 is 256.