Question

The L.C.M. of \(\frac{7}{3},\ \frac{5}{6},\ \frac{14}{9}\) is

• A. \(\frac{70}{18}\)
• B. \(\frac{70}{9}\)
• C. \(\frac{70}{3}\)
• D. 70

Hint:

For fractions, remember: \[ \text{LCM}=\frac{\text{LCM of numerators}}{\text{HCF of denominators}} \] while \[ \text{HCF}=\frac{\text{HCF of numerators}}{\text{LCM of denominators}}. \]

Answer 1

The Correct Option is C

Step 1: Recall the rule for fractions.
The L.C.M. of fractions is found by \[ \text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}} \]

Step 2: List the numerators and denominators.
The fractions are $\dfrac{7}{3}, \dfrac{5}{6}, \dfrac{14}{9}$. Numerators are $7, 5, 14$ and denominators are $3, 6, 9$.

Step 3: Find the LCM of the numerators.
Break them into primes: $7 = 7$, $5 = 5$, $14 = 2 \times 7$. \[ \text{LCM}(7,5,14) = 2 \times 5 \times 7 = 70 \]

Step 4: Find the HCF of the denominators.
Here $3 = 3$, $6 = 2 \times 3$, $9 = 3 \times 3$. The only common factor is $3$. \[ \text{HCF}(3,6,9) = 3 \]

Step 5: Put them in the formula.
\[ \text{LCM} = \frac{70}{3} \]

Step 6: State the answer.
\[ \boxed{\dfrac{70}{3}} \]