LCM(10, 24, 26)
To find the least common multiple (LCM) of 10, 24, and 26, we can proceed as follows:
Factorize each of the numbers into its prime factors:
10 = 2 × 5
24 = 2 × 2 × 2 × 3
26 = 2 × 13
Identify the highest power of each prime factor that appears in any of the numbers:
2 appears at its highest power of 3 (in 24).
3 appears at its highest power of 1 (in 24).
5 appears at its highest power of 1 (in 10).
13 appears at its highest power of 1 (in 26).
Multiply these highest powers to obtain the LCM:
LCM = 2^3 × 3^1 × 5^1 × 13^1 = 8 × 3 × 5 × 13 = 1560
Therefore, the LCM of 10, 24, and 26 is 1560.
To find the LCM (Least Common Multiple) of three numbers, 10, 24, and 26, we can follow these steps:
Step 1: Find the prime factorization of each number.
- Prime factorization of 10: 2 * 5
- Prime factorization of 24: 2 * 2 * 2 * 3
- Prime factorization of 26: 2 * 13
Step 2: Identify the highest power of each prime factor that appears in the factorization of any of these numbers.
- From the prime factorization of 10: 2 * 5
- From the prime factorization of 24: 2 * 2 * 2 * 3
- From the prime factorization of 26: 2 * 13
Step 3: Take the highest powers of the prime factors identified in step 2 and multiply them together.
- Highest power of 2: 2 * 2 * 2 = 8
- Highest power of 3: 3
- Highest power of 5: 5
- Highest power of 13: 13
Step 4: Multiply the highest powers of the prime factors together.
- LCM(10, 24, 26) = 8 * 3 * 5 * 13 = 1560
Therefore, the LCM of 10, 24, and 26 is 1560.
To find the LCM (Least Common Multiple) of 10, 24, and 26, you can use one of the following methods:
Method 1: Prime Factorization Method
1. Start by finding the prime factorization of each number.
- Prime factorization of 10: 2 * 5
- Prime factorization of 24: 2^3 * 3
- Prime factorization of 26: 2 * 13
2. Now, find the highest power of each prime factor that appears in any of the three factorizations.
- The highest power of 2 is 2^3.
- The highest power of 3 is 3.
- The highest power of 5 is 5.
- The highest power of 13 is 13.
3. Multiply all these highest powers together to find the LCM.
LCM(10, 24, 26) = 2^3 * 3 * 5 * 13 = 1560.
Therefore, the LCM of 10, 24, and 26 is 1560.
Method 2: Using a Calculator
You can also use a calculator with the LCM function to find the LCM directly.