Find the LCM of 12,24, and 30
Let's look at the multiples of 30.
30, 60, 90, 120, 150, 180, 210
What is the smallest of these numbers that is evenly divisible by both 12 and 24?
120
Right! :-)
To find the LCM (Least Common Multiple) of 12, 24, and 30, you can follow these steps:
1. Prime Factorization: Write the prime factorization of each number:
- 12 = 2^2 * 3
- 24 = 2^3 * 3
- 30 = 2 * 3 * 5
2. Identify the Highest Powers: Take the highest power of each prime factor from the list above:
- The highest power of 2 is 2^3 = 8
- The highest power of 3 is 3^1 = 3
- The highest power of 5 is 5^1 = 5
3. Multiply the Highest Powers: Multiply the highest powers together:
8 * 3 * 5 = 120
Therefore, the LCM of 12, 24, and 30 is 120.