Find the GCF and LCM of 15 and 50
5, 150
To find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 15 and 50, you can follow these steps:
Step 1: Prime factorize both numbers.
15 = 3 × 5
50 = 2 × 5 × 5
Step 2: Identify the common factors.
The common factor between 15 and 50 is 5.
Step 3: Calculate the GCF.
The GCF of 15 and 50 is 5.
Step 4: Calculate the LCM.
The LCM of 15 and 50 is calculated by multiplying all of the prime factors, including the repeated ones, with the highest exponent.
LCM = 2 × 3 × 5 × 5 = 150
So, the GCF of 15 and 50 is 5, and the LCM is 150.
To find the greatest common factor (GCF) and least common multiple (LCM) of 15 and 50, you can use different methods. I will explain two common ways to solve this problem.
Method 1: Prime Factorization
1. Start by writing the prime factorization of each number.
- The prime factorization of 15 is 3 * 5.
- The prime factorization of 50 is 2 * 5 * 5.
2. Identify the common prime factors.
- The common prime factor is 5.
3. Find the GCF by multiplying the common prime factors.
- GCF = 5.
4. Find the LCM by multiplying all prime factors, both common and unique, for both numbers.
- LCM = 2 * 3 * 5 * 5 = 150.
Method 2: Listing Multiples
1. Start by listing the multiples of each number until you find a common multiple.
- Multiples of 15: 15, 30, 45, 60, 75...
- Multiples of 50: 50, 100, 150...
2. Identify the common multiple.
- The common multiple is 150.
3. Find the GCF by identifying the largest factor that both numbers share.
- Factors of 15: 1, 3, 5, 15
- Factors of 50: 1, 2, 5, 10, 25, 50
- The largest common factor is 5.
4. Find the LCM by dividing the common multiple by the GCF.
- LCM = 150 / 5 = 30.
So the GCF of 15 and 50 is 5, and the LCM is 150.