If three numbers are 2a, 5a and 7a, what will be their LCM?

Options

A. 70a
B. 65a
C. 75a
D. `70a^2`

Answer

To find the Least Common Multiple (LCM) of the numbers 2a, 5a, and 7a, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers**: The given numbers are 2a, 5a, and 7a.

2. **Factor Out Common Terms**: Since all three numbers contain the common factor 'a', we can factor 'a' out. This gives us:
\[ LCM(2a, 5a, 7a) = a \cdot LCM(2, 5, 7) \]

3. **Find the LCM of the Coefficients**: Now, we need to find the LCM of the coefficients 2, 5, and 7. These numbers are all prime and do not share any common factors other than 1.

4. **Calculate the LCM**: The LCM of prime numbers is simply their product:
\[ LCM(2, 5, 7) = 2 \times 5 \times 7 \]

5. **Perform the Multiplication**:
- First, multiply 2 and 5:
\[ 2 \times 5 = 10 \]
- Next, multiply the result by 7:
\[ 10 \times 7 = 70 \]

6. **Combine with the Common Factor**: Now, we can combine this result with the common factor 'a':
\[ LCM(2a, 5a, 7a) = 70a \]

### Final Answer:
The LCM of the numbers 2a, 5a, and 7a is \( 70a \).

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