find the GCF and LCM of 24 ,144 ,100
To find the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of 24, 144, and 100, we can list the prime factors of each number and compare them.
Prime factorization of 24:
24 = 2 * 2 * 2 * 3 = 2^3 * 3
Prime factorization of 144:
144 = 2 * 2 * 2 * 2 * 3 * 3 = 2^4 * 3^2
Prime factorization of 100:
100 = 2 * 2 * 5 * 5 = 2^2 * 5^2
Now, let's determine the GCF. The GCF is the product of the common factors with the least exponent.
GCF:
2^2 * 3 = 4 * 3 = 12
Next, we'll find the LCM. The LCM is the product of the highest powers of all prime factors.
LCM:
2^4 * 3^2 * 5^2 = 16 * 9 * 25 = 3,600
Therefore, the GCF of 24, 144, and 100 is 12, and the LCM is 3,600.
To find the greatest common factor (GCF) and least common multiple (LCM) of the numbers 24, 144, and 100, let's start by finding the prime factorization of each number:
Prime factorization of 24: 2^3 x 3^1
Prime factorization of 144: 2^4 x 3^2
Prime factorization of 100: 2^2 x 5^2
Now, we can find the GCF by taking the smallest exponent for each prime factor that appears in all three numbers:
GCF = 2^2 x 3^1 = 12
To find the LCM, we take the highest exponent for each prime factor that appears in any of the numbers:
LCM = 2^4 x 3^2 x 5^2 = 720
Therefore, the GCF of 24, 144, and 100 is 12, and the LCM is 720.
To find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of three numbers, 24, 144, and 100, follow these steps:
Step 1: Prime factorize each number.
- Prime factorization of 24: 2^3 * 3^1
- Prime factorization of 144: 2^4 * 3^2
- Prime factorization of 100: 2^2 * 5^2
Step 2: Identify the common prime factors.
The common prime factors among the three numbers are 2 and 3.
Step 3: Find the GCF.
The GCF is the product of the common prime factors, raised to the lowest power they appear in any of the numbers.
GCF = 2^2 * 3^1 = 12
Step 4: Find the LCM.
The LCM is the product of all the prime factors, raised to their highest power.
LCM = 2^4 * 3^2 * 5^2 = 720
Therefore, the GCF of 24, 144, and 100 is 12, and the LCM is 720.