The LCM of the three numbers 45 , 25 and 35 is :

Options

A. 1800
B. 1575
C. 1400
D. 1225

Answer

To find the LCM (Least Common Multiple) of the numbers 45, 25, and 35, we can follow these steps:

### Step 1: Prime Factorization
First, we will perform the prime factorization of each number.

- **45**:
- 45 = 3 × 15
- 15 = 3 × 5
- So, 45 = 3² × 5¹

- **25**:
- 25 = 5 × 5
- So, 25 = 5²

- **35**:
- 35 = 5 × 7
- So, 35 = 5¹ × 7¹

### Step 2: Identify the Highest Powers of Each Prime Factor
Next, we will identify the highest power of each prime factor from the factorizations:

- For **3**: The highest power is 3² (from 45).
- For **5**: The highest power is 5² (from 25).
- For **7**: The highest power is 7¹ (from 35).

### Step 3: Calculate the LCM
Now, we will multiply these highest powers together to find the LCM:

\[ \text{LCM} = 3^2 \times 5^2 \times 7^1 \]

Calculating this step-by-step:

1. Calculate \(3^2 = 9\)
2. Calculate \(5^2 = 25\)
3. Now multiply these results with \(7^1 = 7\):

\[ \text{LCM} = 9 \times 25 \times 7 \]

4. First, calculate \(9 \times 25 = 225\)
5. Now multiply \(225 \times 7 = 1575\)

Thus, the LCM of 45, 25, and 35 is **1575**.

### Final Answer:
The LCM of 45, 25, and 35 is **1575**.

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