This document discusses factors, multiples, least common multiples (LCM), and greatest common factors (GCF). It provides examples of finding the multiples of numbers by multiplying them by counting numbers. It also shows how to find the LCM and GCF of two numbers by listing their common multiples or factors and taking the least or greatest. The key steps are to find the multiples of each number, identify their common multiples to determine the LCM, or common factors to determine the GCF.
Helping parents to understand the correct method of teaching their children Algebra / Mathematics / Math can be tricky.
There are many pit-falls in helping children with their homework because many of the ways we were taught are out of date.
Try this simple free online lesson and watch as your child learns how to do Simple Division by following this step-by-step guide.
This presentation is based on CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product
Helping parents to understand the correct method of teaching their children Algebra / Mathematics / Math can be tricky.
There are many pit-falls in helping children with their homework because many of the ways we were taught are out of date.
Try this simple free online lesson and watch as your child learns how to do Simple Division by following this step-by-step guide.
This presentation is based on CCSS.Math.Content.5.OA.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
CCSS.Math.Content.5.OA.A.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product
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The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
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Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
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The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
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10. Let us multiply 1, 2, 3,4, 5, 6, 7, 8, 9, 10, 11, and 12 by 2.
11. We can get the multiples of 2 when we count by 2s.
The numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24 are the
multiples of 2.
12. These are MULTIPLES OF 3.
If we multiple the numbers 1 to 12 by 3, we get the numbers:
3 6 9 12 15 18 21 24 27 30 33 36
We generate the multiples of 3 when we count by 3s.
13. NOTE:
When we multiply the set of counting numbers by 4, we get the
multiples of 4.
When we multiply the set of counting numbers by 5, we get the
multiples of 5.
When we multiply the set of counting numbers by 6, we get the
multiples of 6 and so on.
15. Let us get the multiples of 2 and 3 and their common multiples.
The least of all the common multiples is 6.
MULTIPLES OF 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 …
MULTIPLES OF 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 …
COMMON MULTIPLES OF 2 AND 3: 6, 12, 18, 24…
Hence, 6 is called the least common multiple
or LCM of 2 and 3.
16. Try this! Get the LCM of 3 and 4.
MULTIPLES OF 3:
MULTIPLES OF 4:
COMMON
MULTIPLES OF 3
AND 4:
17. Get the LCM of 6 and 9.
MULTIPLES OF 6:
MULTIPLES OF 9:
COMMON
MULTIPLES OF 6
AND 9:
19. The pupils of Mr. Razon gave the following answers.
1 x 36 = 36 4 x 9 = 36 18 x 2 = 36 6 x 6 = 36 12 x 3 = 36
The numbers 1, 2, 3, 4, 6, 9, 12, 18, and 36 are the factors of 36.
20. Another example:
3 and 8 1 and 24 6 and 4 12 and 2
The numbers 1, 2, 3, 4, 6, 8, 12, and and 24 are the factors of 24.
Give all the pairs of factors of 24.
21. Let us list down the factors of 24 and 36 and their common factors.
Note that 12 is the greatest of all the common factors of 24 and 36.
Factors of 24:
Factors of 36:
COMMON FACTORS
OF 24 AND 36:
1, 2, 3, 4, 6, 8, 12, 24
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 6, 12
Hence, 12 is the greatest common factor of 24 and 36.
22. We can use the PRIME FACTORIZATION METHOD.
36
2 18
x
9
2 x
3 3
x
24
2 12
2
x
x 6
2 x 3
24: 2 x 2 x 2 x 3
36: 2 x 2 x 3 x 3
2 2
x x 3 = 12 GCF = 12
Factor Tree
23. REMEMBER:
a. The numbers that we multiply are called factors.
b. The multiples of a number are the products of the number and the
set of counting numbers.
c. When the common multiples of two numbers are listed in
increasing order, the first number is the LCM.
d. When the factors of two numbers are listed in increasing order,
the last number is the GCF.
