Discussion

What is HCF of 36/75, 48/150 , 72/135?

Answer: A

For fractions the rule inverts between the two halves:

\[ \text{HCF of fractions} = \frac{\operatorname{HCF}(\text{numerators})}{\operatorname{LCM}(\text{denominators})} \]

Numerators first:

\[ \operatorname{HCF}(36,48,72) = 12 \]

Then the denominators, through their prime factors:

\[ 75 = 3 \cdot 5^{2}, \quad 150 = 2 \cdot 3 \cdot 5^{2}, \quad 135 = 3^{3} \cdot 5 \]

\[ \operatorname{LCM} = 2 \cdot 3^{3} \cdot 5^{2} = 1350 \]

\[ \therefore\; \text{HCF} = \frac{12}{1350} \]

Taking the LCM of the numerators and the HCF of the denominators instead gives the LCM of the fractions, which is the usual confusion.

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