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LCM using product notation
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LCM using product notation
      
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Secondary math lessons to learn
'LCM using product notation' for 7th grade

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:

  1. Write each number as a product of prime factors.
  2. 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 these interactive math lessons you will be learning "LCM using product notation" from
7th grade / Number / Multiples Factors Primes in 3 easy steps. The math in our lessons consists of 6 questions that ask you to identify the lowest common multiple (LCM) of 2 numbers using product notation.

Show lesson introduction
1 / 6
Using product notation, the lowest common multiple (LCM) of 16 & 24 is 2⁴ x 3
16 & 24
2⁴ x 3
2 / 6
Using product notation, the LCM of 9 & 18 is 2 x 3²
9 & 18
2 x 3²
3 / 6
Using product notation, the LCM of 12 & 18 is 2² x 3²
12 & 18
2² x 3²
4 / 6
Using product notation, the LCM of 8 & 21 is 2³ x 3 x 7
8 & 21
2³ x 3 x 7
5 / 6
Using product notation, the LCM of 44 & 63 is 2² x 3² x 7 x 11
44 & 63
2² x 3² x 7 x 11
6 / 6
Using product notation, the LCM of 10 & 36 is 2² x 3² x 5
10 & 36
2² x 3² x 5

There are 3 easy math lesson activities in this "LCM using product notation" tutorial. These activities progress step by step to help you the learner gradually master this math topic. The activities are based on "3 stage questioning", a method of learning that quickly and easily builds your confidence as you work through the short series of lessons that strengthen your knowledge of the math that you want to learn.

When you have completed the tutorial for a topic, you should try some of our games before finally doing the test for your chosen topic. See the Help box below for detailed instructions on how to use the lesson activities to help you learn your math more easily.

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How to use our tutorials to learn
'LCM using product notation' for 7th grade

Introduction to the math topic

You start the tutorial with a lesson that introduces the math you will be learning. You will see a set of questions one at a time, and for each question you will see the written answer and also hear the answer to that question.

Repeat the question/answer by clicking on the brown speaker sign. Repeat the question/answer and expand the question graphic by clicking on the question box. Move between questions using the arrow buttons below the question. If there is additional information available for your chosen topic, the "i" button on the left upright bar will be brown on white. Click on the button to load the additional lesson information into the main interface.


Either / Or math lesson

This lesson moves on from the "Introduction" lesson and offers you two possible answers to each question. So, you will see a question then a voice will ask "Is this ... or is it ..." and you will have to choose which of the answers is the one that matches the question.

You choose an answer by clicking or tapping on one of the two answer boxes below the question. You can play the audio for each answer again by clicking on the speaker icon beside the written answer (if robot speech is available and enabled). The program will let you know each time whether you answered correctly. A star will light up red for a wrong answer or white/black for a correct answer.

This lesson asks you the questions in a random order compared to the introduction. At the end of the lesson, you can choose whether to repeat the lesson or move on to the next one.


What is it? math lesson

The final lesson of the tutorial shows you multiple possible answers for each question - you must choose the correct one. You are asked a question and below it are a list of two, three, or four possible written/numeric answers from this topic. Pressing the speaker icon will play the math audio for that answer.

For each picture, click on the answer that matches the question. The program will tell you whether you are right or not. As with the Either / Or activity a system of stars indicate your right and wrong answers. The What is it? lesson will show you all the questions you learned in the Introduction but in a random order.


When you complete the "What is it?" lesson, you can choose whether to go on to play some games with this topic, or whether you want to repeat some or all of the lesson activities in this tutorial. You should expect to get 80% of the answers correct in most of the activities before trying some of the Math games with this topic.

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