The LCM of 15, 20 and 25 is

Options

A. 350
B. 200
C. 300
D. 250

Answer

To find the LCM (Least Common Multiple) of 15, 20, and 25, we can use the prime factorization method. Here’s a step-by-step solution:

### Step 1: Prime Factorization
First, we need to find the prime factorization of each number.

- **15**: The prime factors of 15 are \(3 \times 5\).
- **20**: The prime factors of 20 are \(2^2 \times 5\) (which is \(2 \times 2 \times 5\)).
- **25**: The prime factors of 25 are \(5^2\) (which is \(5 \times 5\)).

### Step 2: List the Prime Factors
Next, we list out all the prime factors we found:

- From 15: \(3^1\), \(5^1\)
- From 20: \(2^2\), \(5^1\)
- From 25: \(5^2\)

### Step 3: Take the Highest Power of Each Prime Factor
To find the LCM, we take the highest power of each prime factor present in the factorizations:

- For \(2\): The highest power is \(2^2\) (from 20).
- For \(3\): The highest power is \(3^1\) (from 15).
- For \(5\): The highest power is \(5^2\) (from 25).

### Step 4: Multiply the Highest Powers Together
Now, we multiply these together to get the LCM:

\[ LCM = 2^2 \times 3^1 \times 5^2 \]

Calculating this step-by-step:

1. \(2^2 = 4\)
2. \(3^1 = 3\)
3. \(5^2 = 25\)

Now, multiply these results together:

\[ 4 \times 3 = 12 \]
\[ 12 \times 25 = 300 \]

### Conclusion
Thus, the LCM of 15, 20, and 25 is **300**.

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