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Secondary math tests for
'LCM using product notation' for 8th grade
8th grade / Number / Multiples Factors Primes / Multiples / LCM using product notation
Show the lowest common multiple of 2 numbers using product notation
To find the lowest common multiple (LCM) of two numbers, you need to find the smallest multiple that both numbers have in common. One way to do this is to use prime factorization and product notation. Here are the steps:
- Write each number as a product of prime factors.
- Then write the prime factors of each number, multiplying each factor by the highest power it appears in either number.
For example:
The prime factorization of one number is 2² x 3 x 5.
The prime factorization of the other number is 2 x 3² x 7.
The product notation is 2² x 3² x 5 x 7.
If required, you can simplify the product notation by multiplying the bases and their respective exponents. For example, 2² x 3² x 5 x 7 = 4 x 9 x 5 x 7 = 1260.
Here's an example of how to find the LCM of 12 and 15 using product notation:
Write each number as a product of prime factors.
- The prime factorization of 12 is 2² x 3
- The prime factorization of 15 is 3 x 5
Write the prime factors of each number in product notation, multiplying each factor by the highest power it appears in either number: 2² x 3 x 5. Note that the factor 5 appears in only one of the numbers but we still include it in the product notation.
To get the LCM as a number you can simplify the product notation by multiplying the bases and their respective exponents.
Therefore, the LCM of 12 and 15 is 2² x 3 x 5 in product notation, which is 60.
In this topic you are asked to use prime factorization to derive the lowest common multiple of 2 numbers and present your answer using product notation.
With our quick math tests you will be revising "LCM using product notation" in 2 simple steps. The math in our tests consists of 16 questions that ask you to identify the lowest common multiple (LCM) of 2 numbers using product notation.
These math tests are designed to round off your learning experience here at Free Math Games by testing whether you can correctly recognize the math you have learned (in the multiple choice test) and that you can correctly enter the correct answers (in the writing test).
Make sure you have chosen the correct topic before starting! Although these tests are timed, try to relax and concentrate on getting the answers right at first - later you can try the tests again more quickly.
The two types of tests are:
- A multiple choice quiz to check your recall of the math
- A writing test to check your math for the selected topic
Key features of our math tests include:
- You can do these tests at home (or at school) without the help of a teacher
- You can repeat our tests as often as you need to improve your scores
- The tests check your comprehension for the topic
- The writing test also checks your ability to write / type math answers for the topic
- The tests use all the questions in a topic, so you will see questions that weren't in the lessons
You should expect to score 8+ / 10 in each test before you select a new topic. It is a good idea to repeat the test for each topic you do after two weeks to "reinforce" the math for that topic
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How to use our math tests for
'LCM using product notation' for 8th grade
- On the settings screen, select the test you would like to take.
- A new screen will open with information concerning the test.
- When you are ready to begin, click "Start the test".
Multiple choice test
This is a multiple choice activity similar to "What is it" in the Math lessons - you are shown a randomly selected question from the topic you are using. A selection of topic answers are displayed as a list. If you click/tap the speaker beside any answer you will hear the audio for that answer.
For each question, you must click on the answer that matches that question. If your answer is correct you will hear a bell and one star will be lit. The next question will be shown. If your answer is wrong, a box will open showing you what the correct answer was.
The test is timed, and the clock starts when you click the Start button. The clock stops when you click your final answer. At the end of your test a screen will tell you how many of the questions you got right and how long you took to complete the test.
Writing test
The writing test checks whether you can type the correct answer using your keyboard. This test is also timed. You can do the test many times until you get a good score. To start the test, click on the "Writing test" sign in the navigation board, then click on the "Start the test" arrow.
A random problem from your selected topic is shown. Beneath the problem there is a white box into which you should type the answer. If you need a little help you can click on the "Help me" button for a tip. Only use the help if you really need to.
If you type the answer correctly your device will automatically light a star. If you have entered your answer and no star lights up, click on the tick or press Enter to check your answer. When you have tried all the questions, a screen will show you how many questions you answered correctly and how long it took.
* Try to score 8 out of 10 in both test before you choose a new topic *
* It is OK to do the tests many times if you need to *
