Answer
Depending on the number each method has its benefits.
Work Step by Step
Method of finding the least common multiple is convenient if the numbers are small so one can quickly find the least common multiple by inspection.
Example: The common multiple for $2$ and $6$ is $6$, because $ 2 \cdot 1 = 2, 2 \cdot 2 = 4, 2 \cdot 3 = 6, \dots$ and $6 \cdot 1 = 6, \dots$.
Method of using multiples of the largest number is quick to determine for small numbers but might take more effort for large numbers since the list will be longer.
Example: The common multiple of $3$ and $5$ is $15$, because $3, 6, 9, 12, 15, 18, \dots$ and $5, 10 ,15, 20, \dots$.
Method of using prime factorization is convenient to use for larger numbers where you find the prime factorization for each number and then simply multiply which appear in greatest number of times in either factorization.
Example: The common multiple of $3$ and $4$ is $12$, because $3 = 3$ and $4 = 2 \cdot 2$. So the LCM is $2 \cdot 2 \cdot 3 = 12$.
