Given that H.C.F. (306, 954, 1314) = 18, find L.C.M. (306, 954, 1314).

Options

A. 1183234
B. 1123238
C. 1183914
D. 1123328

Answer

To find the L.C.M. (Least Common Multiple) of the numbers 306, 954, and 1314 given that their H.C.F. (Highest Common Factor) is 18, we can use the relationship between H.C.F. and L.C.M. which is given by the formula:

\[ \text{L.C.M.}(a, b, c) = \frac{a \times b \times c}{\text{H.C.F.}(a, b, c)} \]

### Step-by-step Solution:

1. **Identify the numbers and H.C.F.**
We have the numbers:
\( a = 306 \)
\( b = 954 \)
\( c = 1314 \)
And we know that:
\( \text{H.C.F.}(306, 954, 1314) = 18 \)

2. **Calculate the product of the numbers.**
We need to calculate the product of the three numbers:
\[ 306 \times 954 \times 1314 \]

3. **Calculate the product.**
First, calculate \( 306 \times 954 \):
\[ 306 \times 954 = 291624 \]
Now, multiply this result by 1314:
\[ 291624 \times 1314 = 383838336 \]

4. **Divide the product by the H.C.F.**
Now, we will divide the product by the H.C.F.:
\[ \text{L.C.M.} = \frac{383838336}{18} \]

5. **Perform the division.**
Dividing \( 383838336 \) by \( 18 \):
\[ \text{L.C.M.} = 21324352 \]

### Final Answer:
Thus, the L.C.M. of 306, 954, and 1314 is \( 21324352 \).