If H.C.F. of 56 and 98 is 14, then its L.C.M. will be

Options

A. 56
B. 98
C. 392
D. 784

Answer

To find the L.C.M. (Least Common Multiple) of two numbers when the H.C.F. (Highest Common Factor) is given, we can use the relationship between H.C.F., L.C.M., and the two numbers. The formula is:

\[ \text{H.C.F.} \times \text{L.C.M.} = \text{a} \times \text{b} \]

where \( a \) and \( b \) are the two numbers.

### Step-by-Step Solution:

1. **Identify the Numbers and H.C.F.**:
- Let \( a = 56 \)
- Let \( b = 98 \)
- Given H.C.F. = 14

2. **Use the Formula**:
- According to the formula:
\[ \text{H.C.F.} \times \text{L.C.M.} = a \times b \]
We can rearrange this to find L.C.M.:
\[ \text{L.C.M.} = \frac{a \times b}{\text{H.C.F.}} \]

3. **Calculate \( a \times b \)**:
- Calculate \( 56 \times 98 \):
\[ 56 \times 98 = 5488 \]

4. **Substitute the Values into the Formula**:
- Now substitute \( a \times b \) and H.C.F. into the formula:
\[ \text{L.C.M.} = \frac{5488}{14} \]

5. **Perform the Division**:
- Calculate \( \frac{5488}{14} \):
\[ 5488 \div 14 = 392 \]

6. **Final Result**:
- Therefore, the L.C.M. of 56 and 98 is:
\[ \text{L.C.M.} = 392 \]

### Summary:
The L.C.M. of 56 and 98 is **392**.