The L.C.M. of 4 and 44 is

Options

A. 4
B. 11
C. 44
D. 176

Answer

To find the Least Common Multiple (L.C.M.) of 4 and 44 using the factorization method, follow these steps:

### Step-by-Step Solution:

1. **Factorize the Numbers:**
- First, we need to factorize both numbers into their prime factors.
- For **4**:
- 4 can be factored as \(2 \times 2\) or \(2^2\).
- For **44**:
- 44 can be factored as \(2 \times 22\).
- Then, factor 22: \(22 = 2 \times 11\).
- So, \(44 = 2 \times 2 \times 11\) or \(2^2 \times 11\).

2. **List the Prime Factors:**
- From the factorization, we have:
- \(4 = 2^2\)
- \(44 = 2^2 \times 11\)

3. **Identify the Common and Unique Factors:**
- The common prime factor is \(2\) (which appears in both factorizations).
- The unique prime factor from 44 is \(11\).

4. **Write the LCM:**
- For the LCM, we take the highest power of each prime factor:
- For \(2\), the highest power is \(2^2\).
- For \(11\), the highest power is \(11^1\).
- Thus, the LCM is:
\[ LCM = 2^2 \times 11 = 4 \times 11 = 44 \]

5. **Conclusion:**
- Therefore, the L.C.M. of 4 and 44 is **44**.

### Final Answer:
The L.C.M. of 4 and 44 is **44**.

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