To find the least common multiple (LCM) of two numbers, you can use the following method:
- List the multiples of each number until you find a common one, or
- 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.