Question

Question 7
Find the least common multiple (LCM) 5 of 15 and .

Answer 1

To find the least common multiple (LCM) of two numbers, you can use the following method:

1. **List the multiples of each number** until you find a common one, or
2. **Use the prime factorization method**.

Let's find the LCM of 5 and 15 using both methods.

### Method 1: Listing Multiples
- **Multiples of 5**: 5, 10, 15, 20, 25, 30, 35, ...
- **Multiples of 15**: 15, 30, 45, ...

The smallest common multiple is 15.

### Method 2: Prime Factorization
- **Prime factorization of 5**: \( 5^1 \)
- **Prime factorization of 15**: \( 3^1 \times 5^1 \)

To find the LCM, take the highest power of each prime:
- For the prime number 3: \( 3^1 \)
- For the prime number 5: \( 5^1 \)

Now multiply these together:
\[ LCM = 3^1 \times 5^1 = 3 \times 5 = 15 \]

### Conclusion
The least common multiple (LCM) of 5 and 15 is **15**.