Question

What is the LCM of the $\dfrac{3}{5}$ and $\dfrac{1}{3}$?

Answer 1

Hint: We need to find the least common multiple of $\dfrac{3}{5}$ and $\dfrac{1}{3}$. First, we need to find the LCM of the numerators and the GCD of the denominators. For fractions we need to complete both steps to find the total LCM.

Complete step by step solution:
We need to find the LCM of $\dfrac{3}{5}$ and $\dfrac{1}{3}$. LCM stands for least common multiple.
For fractions the rules of LCM apply only for the numerator parts of the fractions and for the denominator part we follow the GCD of the digits.
In the case of $\dfrac{3}{5}$ and $\dfrac{1}{3}$, we have 3 and 1 as numerators.
We find the LCM of 1 and 3. They are co-primes. Therefore, the LCM is the multiplication of those numbers.
The LCM of the numerators is $1\times 3=3$.
We also have 3 and 5 as denominators.
We find the GCD of 3 and 5. They are co-primes. Therefore, the GCD is 1.
Therefore, the LCM of the $\dfrac{3}{5}$ and $\dfrac{1}{3}$ is $\dfrac{3}{1}=3$.

Note: We need to remember that the LCM has to be only one number. It is the least common multiple of all the given numbers. If the given numbers are prime numbers then the LCM of those numbers will always be the multiple of those numbers. These rules follow for both integers and fractions.