Question

Find the LCM of the numbers: \(\frac{4}{9}, \frac{8}{15}, \frac{6}{9}, \frac{12}{21}, \frac{14}{33}\)

• A. \(\frac{160}{3}\)
• B. \(\frac{168}{3}\)
• C. 52
• D. 56

Hint:

LCM of fractions = LCM(numerators)/HCF(denominators)

Answer 1

The Correct Option is D

Step 1: Simplify each fraction.
\(\frac{4}{9}\) (already simplified).
\(\frac{8}{15}\) (already simplified).
\(\frac{6}{9} = \frac{2}{3}\).
\(\frac{12}{21} = \frac{4}{7}\).
\(\frac{14}{33}\) (already simplified).
So fractions: \(\frac{4}{9}, \frac{8}{15}, \frac{2}{3}, \frac{4}{7}, \frac{14}{33}\). Step 2: Recall LCM formula for fractions.
LCM of fractions = \(\frac{\text{LCM of numerators}}{\text{HCF of denominators}}\). Step 3: Find LCM of numerators.
Numerators: 4, 8, 2, 4, 14.
LCM(4,8) = 8. LCM(8,2) = 8. LCM(8,4) = 8. LCM(8,14) = 56.
So LCM of numerators = 56. Step 4: Find HCF of denominators.
Denominators: 9, 15, 3, 7, 33.
HCF(9,15) = 3. HCF(3,3) = 3. HCF(3,7) = 1. HCF(1,33) = 1.
So HCF of denominators = 1. Step 5: Compute LCM.
LCM = \(\frac{56}{1} = 56\).