LCM of 2.5,.075,.0015=

Options

A. `.15`
B. `.075`
C. `.75`
D. `7.5`

Answer

To find the LCM of the numbers 2.5, 0.075, and 0.0015, we can follow these steps:

### Step 1: Convert the decimal numbers to fractions
- 2.5 can be expressed as \( \frac{25}{10} \)
- 0.075 can be expressed as \( \frac{75}{1000} \)
- 0.0015 can be expressed as \( \frac{15}{10000} \)

### Step 2: Identify the numerators and denominators
- The numerators are 25, 75, and 15.
- The denominators are 10, 1000, and 10000.

### Step 3: Find the LCM of the numerators
To find the LCM of 25, 75, and 15, we can use the prime factorization method:
- \( 25 = 5^2 \)
- \( 75 = 3 \times 5^2 \)
- \( 15 = 3 \times 5 \)

The LCM is found by taking the highest power of each prime factor:
- For 3: highest power is \( 3^1 \)
- For 5: highest power is \( 5^2 \)

Thus, the LCM of the numerators is:
\[ \text{LCM} = 3^1 \times 5^2 = 3 \times 25 = 75 \]

### Step 4: Find the HCF of the denominators
To find the HCF of 10, 1000, and 10000:
- The prime factorization of 10 is \( 2^1 \times 5^1 \)
- The prime factorization of 1000 is \( 2^3 \times 5^3 \)
- The prime factorization of 10000 is \( 2^4 \times 5^4 \)

The HCF is found by taking the lowest power of each prime factor:
- For 2: lowest power is \( 2^0 \) (not present in 10)
- For 5: lowest power is \( 5^1 \)

Thus, the HCF of the denominators is:
\[ \text{HCF} = 5^1 = 5 \]

### Step 5: Calculate the LCM of the original numbers
Now, we can find the LCM of the original numbers using the formula:
\[ \text{LCM} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} \]
Substituting the values we found:
\[ \text{LCM} = \frac{75}{5} = 15 \]

### Final Answer
The LCM of 2.5, 0.075, and 0.0015 is **15**.

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