Consider the fractions \frac{12}{25}, \frac{18}{35}, and \frac{24}{55}. Which of the follo… — State PSC Exam

Consider the fractions $\frac{12}{25}$ , $\frac{18}{35}$ , and $\frac{24}{55}$ . Which of the following statements are mathematically correct regarding their Highest Common Factor (HCF) and Least Common Multiple (LCM)?

The HCF of the given fractions is $\frac{6}{1925}$ .Answer
The LCM of the given fractions is $\frac{72}{5}$ .Answer
C
The HCF of the given fractions is $\frac{72}{5}$ .
D
The LCM of the given fractions is $\frac{6}{1925}$ .

Answer

The correct statements are that the HCF of the fractions is

\frac{6}{1925}

and the LCM of the fractions is

\frac{72}{5}

The correct statements properly evaluate the formulas for fractions: the HCF of a set of fractions is the HCF of their numerators divided by the LCM of their denominators, and the LCM of a set of fractions is the LCM of their numerators divided by the HCF of their denominators.

Step-by-Step Solution

Find the HCF and LCM of the numerators (

12, 18, 24

HCF(

12, 18, 24

) =

6

, and LCM(

12, 18, 24

) =

72

These values are required for the numerator positions in the fraction HCF and LCM formulas.

Find the HCF and LCM of the denominators (

25, 35, 55

HCF(

25, 35, 55

) =

5

, and LCM(

25, 35, 55

) =

5^2 \times 7 \times 11 = 1925

These values are required for the denominator positions in the fraction HCF and LCM formulas.

Calculate the HCF of the fractions.

HCF =

\frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{6}{1925}

This determines the validity of the HCF statements.

Calculate the LCM of the fractions.

LCM =

\frac{\text{LCM of numerators}}{\text{HCF of denominators}} = \frac{72}{5}

This determines the validity of the LCM statements.

Key Concept

Highest Common Factor (HCF) and Least Common Multiple (LCM) of Fractions

Question

Answer

Step-by-Step Solution

Key Concept

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