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

Reduce the fractions first: $\frac{4}{9},\frac{8}{15},\frac{2}{3},\frac{4}{7},\frac{14}{33}$. The LCM of fractions is $\frac{\text{LCM of numerators}}{\text{HCF of denominators}}=\frac{\text{LCM}(4,8,2,4,14)}{\text{HCF}(9,15,3,7,33)}=\frac{56}{1}=56$. Without reducing, the numerators have LCM 168 and the denominators HCF 3, giving the same $\frac{168}{3}=56$. Dividing by the LCM of the denominators instead of their HCF is the usual mistake.