Find the lowest perfect squared number that is divisible by 12, 16, 20 and 24
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.
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.
Step 1: Find the LCM of 12, 16, 20, and 24.
Prime factorization of each number:
- 12 = 2^2 * 3
- 16 = 2^4
- 20 = 2^2 * 5
- 24 = 2^3 * 3
LCM: The LCM should include the highest power of each prime factor involved. So, the LCM can be found by multiplying the highest powers of 2, 3, and 5 occurring in the prime factorization of the given numbers:
LCM = 2^4 * 3 * 5 = 240
Step 2: Find the smallest perfect square greater than or equal to 240.
Taking the square root of 240, we find that the square root lies between 15 and 16. So, the smallest perfect square greater than or equal to 240 is 16^2 = 256.
Therefore, the lowest perfect squared number that is divisible by 12, 16, 20, and 24 is 256.