To find the LCM (Least Common Multiple) of the numbers 779, 943, and 123, we can follow these steps:
### Step 1: Prime Factorization
First, we need to find the prime factorization of each number.
- **For 779**:
- 779 can be factored into prime numbers as follows:
- 779 = 41 × 19
- **For 943**:
- 943 can be factored into prime numbers as follows:
- 943 = 41 × 23
- **For 123**:
- 123 can be factored into prime numbers as follows:
- 123 = 41 × 3
### Step 2: Identify Unique Prime Factors
Next, we identify all the unique prime factors from the factorizations we obtained:
- The unique prime factors are: 41, 19, 23, and 3.
### Step 3: Calculate the LCM
To calculate the LCM, we take the highest power of each prime factor that appears in any of the factorizations:
- For 41, the highest power is \(41^1\).
- For 19, the highest power is \(19^1\).
- For 23, the highest power is \(23^1\).
- For 3, the highest power is \(3^1\).
Now, we multiply these together to find the LCM:
\[
\text{LCM} = 41^1 \times 19^1 \times 23^1 \times 3^1
\]
### Step 4: Perform the Multiplication
Now we perform the multiplication step-by-step:
1. Multiply 41 and 19:
\[
41 \times 19 = 779
\]
2. Multiply the result by 23:
\[
779 \times 23 = 17,917
\]
3. Finally, multiply the result by 3:
\[
17,917 \times 3 = 53,751
\]
### Conclusion
Thus, the LCM of 779, 943, and 123 is **53,751**.
