Find the LCM of 15, 25 and 29.
A. 2335
B. 3337
C. 2175
D. 2375

Options

A. A
B. B
C. C
D. D

Answer

To find the LCM (Least Common Multiple) of the numbers 15, 25, and 29, we can follow these steps:

### Step 1: Prime Factorization
- First, we need to find the prime factorization of each number.
- **15** can be factored into \(3 \times 5\).
- **25** can be factored into \(5^2\).
- **29** is a prime number, so it remains as \(29\).

### Step 2: Identify the Highest Powers
- Next, we take the highest power of each prime number that appears in the factorizations:
- The prime factors we have are \(3\), \(5\), and \(29\).
- The highest power of \(3\) is \(3^1\) (from 15).
- The highest power of \(5\) is \(5^2\) (from 25).
- The highest power of \(29\) is \(29^1\) (from 29).

### Step 3: Calculate the LCM
- Now, we multiply these highest powers together to find the LCM:
\[ \text{LCM} = 3^1 \times 5^2 \times 29^1 \]
\[ = 3 \times 25 \times 29 \]

### Step 4: Perform the Multiplication
- First, calculate \(3 \times 25\):
\[ 3 \times 25 = 75 \]
- Next, multiply this result by \(29\):
\[ 75 \times 29 = 2175 \]

### Conclusion
- Therefore, the LCM of 15, 25, and 29 is **2175**.

### Matching with Options
- The correct answer from the options provided is **C. 2175**.

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