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.

for this week’s blog post I decided to chose how to find the greatest common factor, of two numbers

for our example, we will be using 60 and 24 for our numbers

our first step is to use prime factorization to find out our prime numbers

60 has the prime factors of 2², 3, 5

24 has the prime factors of 2³, 3

next step is to single out what prime factors these two numbers share in common with each other.

the answer is 2² and 3

the next step is to use multiplication to multiply these two numbers to give us our answer of what the GCM is for these two numbers

answer is 12 as 2x2x3 is 12

I chose this concept for my blog post because I realized I haven’t completed a blog post on this concept, and finding the GCM is one of my favorite things that our class has done so far.

For this week’s blog post, I am choosing to demonstrate how to find the rule of a pattern with x and y coordinates

Step number 1:  Find your pattern

For this example we will be using the example of 6,9,12,15,18

Step 2: Identify what your pattern is

as we can see our pattern starts at 6, and is going up by 3 each time.

so we will make a new pattern but starting at 3 to put under our existing pattern so it should look like this:

6,9,12,15,18

3,6,9,12,15

now all we need to do is plug what we have into a equation also known as our rule

our equation will start off with how much our patter is going up (or down) by.

so for us with the pattern we have, the rule will be starting off with 3x

after this, we just need to state how much it takes our second pattern to get to our original pattern.

since our first pattern started with 6, and our second pattern started with 3 it would take 3 to get from 3 to 6 so we will put this in our equation too.

our final equation will be

3x + 3 = y

and this is how we find our rule, using a pattern.

today I am going to explain how to solve a polynomial using the rectangle algebra tile method

the first step is to find your polynomial

ours will be x+3 -x +5

our second step will be for us to draw out our rectangle diagram

our third step will be to plug in our polynomial to our rectangle diagram. As you may know, a x² is in the shape of a large square, and a x is in the shape of a skinny and long rectangle and our constant will be a small square and remember that negative numbers are not colored in. Our diagram should now look like this:

next is to simply make the rectangle, and now wherever you see a line in between the algebra tiles, just draw a straight line through, like this:

as you can see it gives us a broken down rectangle that has different algebra tiles in it, and one of the last things you have to do is just list what you have by counting your tiles out. Something to always remember is if you have negative tiles it will make whatever is below it negative if it is a positive that it is going across with, but if it is a negative it will be positive, because we are using multiplication in this rectangle strategy, so we must also follow the rules of multiplication.

the answer would end up being, x² + x -6

I chose to use this topic for this weeks blog post because I felt as though it is a strategy that I understand clearly and thoroughly.

Public broadcasting is a broadcasting service provided and funded by the government, and is free for everyone in for example Canada with CBC, to use. Canadas public broadcaster has been CBC since 1932, and they have been the only one as well. In 1932, CBC was launched but it was first named CRBC but got changed to CBC later. in 1962, the first live television election happened on CBC, in Canada. An advantage of public broadcasting is that it is funded by the government, meaning that the people making the media wont be focused on advertising and their funding, so they can be more focused on viewers. Some people may not agree with public broadcasting, because they are funded by the government, and what is released has to be approved by them so one may feel like public broadcasting cannot voice their true opinion. Public broadcasting can appeal to a modern audience, because there is a lot to offer on public broadcasting, and a lot of different topics about things that certain people will like and other may not like, but luckily there is even more topics that one may be interested in.

in trigonometry this week, we learned about right triangles

right triangles are a triangle with a 90 degree corner, or when you are able to fit a square in one of the corners.

like such

this is a right triangle because the side that has a square in it equals 90 degrees

other important things to note are what each of the sides of the triangles are labeled as.

side H, also known as the hypotenuse is the side straight across from the 90 degree angle

so as you can see here if you started drawing a line in the corner of the square, it would end up on the top side making it our hypotenuse.

we also must know what our reference angle is, or theta to know what we call our adjacent side.

our reference angle can be in any corner except the 90 degree corner

so say we put it in the bottom right corner.

if that is where our reference angle is, the adjacent side would be the side going to the left of the reference angle. you would know this because if the top side is our hypotenuse, it cannot be the adjacent as well.

to find our last side, we just find the last side left, which would be the left side going vertical, and this is the side we would call our opposite side.

I chose this topic to do my refection on because I felt that it was the topic that I understood the most.

photo from

21,615 Right Triangle Images, Stock Photos & Vectors | Shutterstock