State the GCF and LCM of 54 of 24. PAR 6.5, PAR 6.2
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1 point
GCF: 5 LCM: 18
GCF: 18 LCM: 5
GCF: 6 LCM: 216
GCF: 216 LCM: 6
GCF: 6 LCM: 216
To find the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of 54 and 24, we need to find the prime factorizations of both numbers.
The prime factorization of 54 is 2 * 3 * 3 * 3, which can be written as 2 * 3^3.
The prime factorization of 24 is 2 * 2 * 2 * 3, which can be written as 2^3 * 3.
To find the GCF, we need to determine the highest power of each common prime factor. In this case, the highest power of 2 is 2^3, and the highest power of 3 is 3.
Therefore, the GCF of 54 and 24 is 2^3 * 3, which is equal to 24.
To find the LCM, we need to determine the lowest power of each prime factor that appears in either number. In this case, the lowest power of 2 is 2^3, and the lowest power of 3 is 3^3.
Therefore, the LCM of 54 and 24 is 2^3 * 3^3, which is equal to 216.
So, the correct answer is:
GCF: 24
LCM: 216
To find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of two numbers, you can use prime factorization.
Let's start with the GCF of 54 and 24. To find the GCF, we need to find the largest common factor of both numbers. Here's how you can do it:
Step 1: Find the prime factorization of each number.
- The prime factorization of 54 is 2 * 3 * 3 * 3 = 2 * 3^3.
- The prime factorization of 24 is 2 * 2 * 2 * 3 = 2^3 * 3.
Step 2: Identify the common factors. In this case, the common factors are 2 * 3 = 6.
Step 3: Take the product of the common factors. The GCF of 54 and 24 is 6.
Now let's find the LCM of 54 and 24. To find the LCM, we need to find the smallest number that is divisible by both numbers. Here's how you can do it:
Step 1: Find the prime factorization of each number.
- The prime factorization of 54 is 2 * 3 * 3 * 3 = 2 * 3^3.
- The prime factorization of 24 is 2 * 2 * 2 * 3 = 2^3 * 3.
Step 2: Take the highest power of each prime factor. In this case, we take the highest power of 2 and 3, which is 2^3 and 3^3.
Step 3: Take the product of the highest powers of the prime factors. The LCM of 54 and 24 is 2^3 * 3^3 = 8 * 27 = 216.
Therefore, the GCF of 54 and 24 is 6 and the LCM is 216.
Since none of the answer choices provided match the correct GCF and LCM, none of those options are correct.