The LCM of 145 and 87 is:

Options

A. 580
B. 725
C. 290
D. 435

Answer

To find the LCM (Least Common Multiple) of 145 and 87, we can follow these steps:

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

- **145** can be factored as:
- 145 = 29 × 5 (since 29 is a prime number and 5 is also a prime number)

- **87** can be factored as:
- 87 = 29 × 3 (since 29 is a prime number and 3 is also a prime number)

### Step 2: Identify Unique Prime Factors
Next, we list all the unique prime factors from both numbers:
- From 145: 29, 5
- From 87: 29, 3

The unique prime factors are: 29, 5, and 3.

### Step 3: Take the Highest Power of Each Prime Factor
Now, we take the highest power of each prime factor:
- For 29: The highest power is \(29^1\)
- For 5: The highest power is \(5^1\)
- For 3: The highest power is \(3^1\)

### Step 4: Calculate the LCM
Now, we multiply these together to find the LCM:
\[ \text{LCM} = 29^1 \times 5^1 \times 3^1 = 29 \times 5 \times 3 \]

Calculating this step-by-step:
1. First, calculate \(29 \times 5 = 145\).
2. Then, multiply that result by 3:
\[ 145 \times 3 = 435 \]

### Final Answer
Thus, the LCM of 145 and 87 is **435**.

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