The LCM of 94, 188 and 235 is :

Options

A. 705
B. 1880
C. 940
D. 470

Answer

To find the LCM (Least Common Multiple) of the numbers 94, 188, and 235, we will follow these steps:

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

- **94**:
- 94 can be divided by 2 (the smallest prime number):
- \( 94 \div 2 = 47 \)
- 47 is a prime number.
- So, the prime factorization of 94 is \( 2^1 \times 47^1 \).

- **188**:
- 188 can also be divided by 2:
- \( 188 \div 2 = 94 \)
- We already know the factorization of 94:
- \( 94 = 2^1 \times 47^1 \)
- Therefore, \( 188 = 2^2 \times 47^1 \).

- **235**:
- 235 can be divided by 5:
- \( 235 \div 5 = 47 \)
- So, the prime factorization of 235 is \( 5^1 \times 47^1 \).

### Step 2: Identify the Highest Powers
Next, we identify the highest powers of each prime factor from the factorizations:

- For the prime number **2**:
- The highest power is \( 2^2 \) (from 188).

- For the prime number **47**:
- The highest power is \( 47^1 \) (common in all three numbers).

- For the prime number **5**:
- The highest power is \( 5^1 \) (from 235).

### Step 3: Calculate the LCM
Now, we can calculate the LCM by multiplying the highest powers of all prime factors together:

\[ \text{LCM} = 2^2 \times 47^1 \times 5^1 \]

Calculating this step-by-step:

1. Calculate \( 2^2 = 4 \).
2. Multiply by \( 47 \):
\[ 4 \times 47 = 188 \]
3. Multiply by \( 5 \):
\[ 188 \times 5 = 940 \]

Thus, the LCM of 94, 188, and 235 is **940**.

### Final Answer
The LCM of 94, 188, and 235 is **940**.

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