The L.C.M of 3.0,0.09 and 2.7

Options

A. 2.7
B. 0.27
C. 0.027
D. 27

Answer

To find the L.C.M (Least Common Multiple) of the decimal numbers 3.0, 0.09, and 2.7, we will first convert them into whole numbers by eliminating the decimals. Let's go through the steps:

### Step 1: Convert the decimals to whole numbers
- 3.0 can be multiplied by 10 to get 30.
- 0.09 can be multiplied by 100 to get 9.
- 2.7 can be multiplied by 10 to get 27.

So, we have:
- 3.0 → 30
- 0.09 → 9
- 2.7 → 27

### Step 2: Find the prime factorization of each number
- **30**:
- 30 = 2 × 3 × 5
- **9**:
- 9 = 3 × 3 = 3²
- **27**:
- 27 = 3 × 3 × 3 = 3³

### Step 3: Identify the highest powers of each prime factor
Now, we will take the highest power of each prime factor from the factorizations:
- For the prime factor **2**, the highest power is 2¹ (from 30).
- For the prime factor **3**, the highest power is 3³ (from 27).
- For the prime factor **5**, the highest power is 5¹ (from 30).

### Step 4: Calculate the L.C.M
Now, we can calculate the L.C.M by multiplying these highest powers together:
- L.C.M = 2¹ × 3³ × 5¹
- L.C.M = 2 × 27 × 5
- L.C.M = 2 × 135
- L.C.M = 270

### Step 5: Adjust for the decimal places
Since we multiplied the original numbers by 10 and 100, we need to adjust the L.C.M by dividing it by 100 (as we multiplied 0.09 by 100):
- L.C.M = 270 / 100 = 2.7

Thus, the L.C.M of 3.0, 0.09, and 2.7 is **2.7**.

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