\(A\) is the LCM of \(\frac{3}{4}\) and \(\frac{9}{16}\), and \(B\) is the HCF of \(\frac{16}{9}\) and \(\frac{4}{27}\). What is the value of \(A+B\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{259}{108}\)
For fractions in lowest terms, LCM \(=\displaystyle\frac{\text{LCM of numerators}}{\text{HCF of denominators}}\) and HCF \(=\displaystyle\frac{\text{HCF of numerators}}{\text{LCM of denominators}}\).
\(A=\displaystyle\frac{\text{LCM}(3,9)}{\text{HCF}(4,16)}=\frac{9}{4}\)
\(B=\displaystyle\frac{\text{HCF}(16,4)}{\text{LCM}(9,27)}=\frac{4}{27}\)
\(A+B=\displaystyle\frac{9}{4}+\frac{4}{27}=\frac{243+16}{108}\)
\(=\displaystyle\frac{259}{108}\)
The value of \(A+B\) is \(\frac{259}{108}\).