What is the L.C.M of 12 28 and 49
The least common multiple (LCM) of 12, 28, and 49 is 1,176.
To find the Least Common Multiple (LCM) of the given numbers (12, 28, and 49), we can follow these steps:
Step 1: Find the prime factors of each number.
- Prime factors of 12: 2, 2, 3
- Prime factors of 28: 2, 2, 7
- Prime factors of 49: 7, 7
Step 2: Determine the highest power of each prime factor that appears in any of the numbers.
- Highest power of 2: 2^2 = 4
- Highest power of 3: 3^1 = 3
- Highest power of 7: 7^2 = 49
Step 3: Multiply all the highest powers together to find the LCM.
LCM = 2^2 * 3^1 * 7^2
LCM = 4 * 3 * 49
LCM = 588
Therefore, the LCM of 12, 28, and 49 is 588.
To find the least common multiple (LCM) of three numbers, such as 12, 28, and 49, we can follow these steps:
Step 1: Prime factorize each number.
- The prime factorization of 12 is 2^2 * 3^1.
- The prime factorization of 28 is 2^2 * 7^1.
- The prime factorization of 49 is 7^2.
Step 2: Write down all the prime factors with their highest powers.
- The prime factors with their highest powers are 2^2 * 3^1 * 7^2.
Step 3: Multiply all these prime factors together.
2^2 * 3^1 * 7^2 = 4 * 3 * 49 = 588.
The LCM of 12, 28, and 49 is 588.