How can you find the least common multiple using prime factorization?
See process below:
Let's come up with a problem so that I can show you the process.
What is the least common multiple of 12 and 9?
Let's prime factor each of the numbers:
12's prime factors are
9's prime factors are
Now make a chart with both of the numbers:
This is where it gets a little tricky. What we're going to is find the lowest number in our prime factorization. That number is
Obviously, 12 has more 2's because 9 has none.
Now what's the other number in our prime factorization?
9 has more 3's than 12, so I am going to cross out the other 3. We only want the part with the most threes.
Put all of the highlighted numbers down into one multiplication problem:
36 is the least common multiple between 12 and 9.
This is a really helpful video on YouTube about this topic:least common multiple