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finding the least common multiple (lcm) the easy way!

3/21/2020

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You have heard the term LCM in Math from the time you are in elementary school.
Math teachers will often tell you to find the LCM before you can do other mathematical things.
But what is LCM? And when do you use it?

Think back to Grade 5 when your teacher asked you to “FIND THE LCM OF 4 AND 6. You may have sat thee for a while scratching your head trying to remember EXACTLY what that meant.
LCM

LCM stands for Least Common Multiple.
If you take each word, one by one, it becomes a little more clear.
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LEAST
You have heard this word long before Grade 5.
What number is LEAST from the numbers 3, 5 and 1?
Well, it is the number that is the smallest.
So whenever you hear LEAST, you think the number that is the smallest
​in a set of given numbers.

COMMON
You have also heard this word long before Grade 5.
And if you watched Sesame Street growing up, you may have come across this as well.
Which letters of the alphabet in these two words have a letter in COMMON:  ANT &  CAT?
It is the letter ‘A’ and the letter ‘T’.
The same way you can find common letters in two words,
you can find common numbers in multiples.

MULTIPLE
This word almost sounds like the word MULTIPLY.
That is because Multiples from our times tables.
The Multiples of 4 are 4, 8, 12, 16, 20 … 
The Multiples of 6 are 6, 12, 18, 24, 30, …
​
When you look at the timetable grid below, all numbers are MULTIPLES:

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LEAST COMMON MULTIPLE

So now, the LEAST COMMON MULTIPLE, or LCM, is the number that is 
1) The Smallest (LEAST), 
2) The Same (Common) and

when you list out the multiples of two or more numbers.

Let's find the LCM of 4 and 6.

The easiest way to find the LCM of two numbers is to:

STEP 1) List the multiples of each number.
     Look in the multiplication table above to find them. Write about 5 or 6 of them out.

4:      4, 8, 12, 16, 20, 24, 28, 32,...
6:      6, 12, 18, 24, 30, 36, 42, ..

STEP 2) Find the multiples in each list that are COMMON (the same)

4:      4, 8, 12, 16, 20, 24, 28, 32,...
6:      6, 12, 18, 24, 30, 36, 42, ..

Common multiples: 12, 24


STEP 3) Write down the SMALLEST (Least) Common Multiple

LCM:     12  (answer)
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Now you have the steps to find the LCM of a set of numbers. You will need this skill when you are adding and subtracting fractions in the future

Make sure you practice this skill in order to improve your knowledge. Practice is key!

              Try the following for practice: 
              FIND THE LCM of
​              a) 5 and 6   b) 10 and 6    c) 6 and 8    d) 8 and 12
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Circle theorems in 3 minutes

3/15/2020

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Instead of hurting your head about all of the circle theorems, have a look at the above video. In three minutes you will learn the ins-and-outs of all of the different theorems that exist relating to circles.

https://www.youtube.com/watch?v=XUus6-9E9sQ

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5 Ways to improve your math scores

3/15/2020

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​1.  Write out your work. 

This may seem simple, but writing out your work in Mathematics and showing your steps is an integral part of doing well in math. It helps you to take a complicated problem, and break it down into smaller pieces. This not only allows you to check step by step where you may have made an error, but also will cut down on the time taken to complete a question. All of this leads to better grades. When you break a problem down into steps, you will increase your understanding of the concepts behind the question.

2.  focus on what you don't understand.

Focusing on a question you don't understand, believe it or not, may end up giving you the greatest benefit. When you get a question wrong, circle it or highlight it. Then you can come back to it and review it. Focus on your topics and questions where you are the least confident and spend a little extra time at home or on the weekends on these areas. This could include checking out videos on the math topic on YouTube for a clearer understanding or checking out Math Forums or other Blogs online. There are literally thousands of videos and websites that are out there that can clarify any topic you are struggling with. You can pause and play a video to ensure understanding when you are stuck on a particular topic. Start to learn from your challenges and failures. Embrace the struggle and try problems outside your comfort zone. This is how we learn best! 

3.  practice, practice, practice

The old saying of "practice makes perfect" often pertains to mathematics. After learning a given topic, it is wise to practice several in order to ensure you have gotten the concept down. As you do homework and get a problem correct, have your index cards nearby and make up a new question that is similar by changing numbers, and see if you can solve that one, too. Past papers of examination questions are also helpful in going over skills and concepts for practice. 

4.  be patient

Make sure that you don not rush through a Math problem. Take your time as you go through each step in order to ensure a correct answer at the end. Rushing through Math problems just to get them done so that you can watch television, get on your phone or login to a social media account can often lead to silly mistakes. Set aside a specific amount of time when you set out to do your Math assignments (at least an hour) so that you know the time allocated to completing your problems. This way you won't set out to rush them through.

5.  ask for help or try helping someone else.

There are many people you have access to that would be glad to lend assistance. Teachers (including the ones that don't teach you) during lunch, breaktime and after school are always willing to lend assistance. Friends in your class or social group may understand a topic you don't. Instead of wasting time socializing or doing nothing, spend some lunchtimes going over some questions you have difficulty with.

Also, often, the best form of learning is teaching. It is often said that f you want to really understand something, try teaching it to someone else. Always questioning along the way will also help. These questions can be ‘Why did you do that?’ and ‘How did you know this?’ will often cause you to question your understanding of a concept in Math and in turn add depth to your understanding. It will also help you to develop the extremely important skill of articulating your thoughts on complex or confusing issues.
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    Author

    C. W. R. Higgs is the author of the Bahamian Mathematics Workbook series. He has a passion for Math and helping students to achieve their greatest potential.

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