Today I will be explaining how to find the least common multiple of two numbers.
So what is the least common multiple (lcm)? The lcm is basically when we have two numbers in this instance, and we find what number that they both share that is a multiple of each.
our first example we will use is 24, and 80. During finding out the lcm, we will use other strategies like prime factorization, and we can even use the gcm to help us find out our lcm.
The first step is to get our prime factorization of 24, which is 2,2,3,2 and 80, which is 2,2,2,2,5
We wont be using the gcm strategy for the first example.
What we now do is we combine the like terms into one. So we have 3 2s in the first prime factorization, and 4 in the second. So we just need to basically put the 3 that we have in the first factorization into the second one, but note that when we combine them, we just get 1 of the same number, so we will be getting 2,2,2,2. because the 3 2s went into the other 3 that they both shared, and it makes only one copy as you remember, and then we have 3 2s, with one more 2 remaining for our factorization of 80.
after this, we put our other factors with no other common terms into the equation, so we will have 2,2,2,2,3,5.
After that, we just have to multiply them all together which will result in our answer for our lcm. The lcm of 80 and 24 is 240.
Our next example will be 75 and 120. So as we did in the first example we will need to use our prime factorization.
75s prime factors: 3,5,5
120s prime factors: 2,2,2,3,5
We will be using the gcm to find our lcm in this example. So we can find our gcm which will be 3×5 because those are our common terms. which is 15. After we find the gcm, we can use all the terms we didn’t use in finding our gcm and multiply them into the equation. So it would be:
15x2x2x2x5 which equals 600, which is also our lcm. As you can see, we found the lcm using the gcf, which can be useful in some situations but both ways work for finding our lcm.
The reason that I chose to use the lcm for this weeks blog post, especially way after we learned it is because since the midterm was coming up, I needed to review and I came across the lcm and gcf strategies and the whole idea of them was a bit foggy in my head, so I reviewed how to do them, and then after I really remembered how much I enjoyed doing them, so I chose to do my blog post on them.