Question : Find the LCM of reciprocals of 22 and 16.
Option 1: $\frac{1}{2}$
Option 2: $\frac{1}{3}$
Option 3: $\frac{1}{6}$
Option 4: $\frac{1}{4}$
Correct Answer: $\frac{1}{2}$
Solution :
The reciprocals of 22 and 16 are $\frac{1}{22}$ and $\frac{1}{16}$ respectively.
The least common multiple (LCM) of two fractions is the LCM of their numerators divided by the greatest common divisor (GCD) of their denominators.
However, since the numerators of both fractions are 1 (the LCM of 1 and 1 is 1), the GCD of the denominators 22 and 16 is 2.
Therefore, the LCM of $\frac{1}{22}$ and $\frac{1}{16}$ is $\frac{1}{2}$.
Hence, the correct answer is $\frac{1}{2}$.
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