# MA.6.NSO.3.1

Given a mathematical or real-world context, find the greatest common factor and least common multiple of two whole numbers.

### Examples

Example: Middleton Middle School’s band has an upcoming winter concert which will have several performances. The bandleader would like to divide the students into concert groups with the same number of flute players, the same number of clarinet players and the same number of violin players in each group. There are a total of 15 students who play the flute, 27 students who play the clarinet and 12 students who play the violin. How many separate groups can be formed?

Example: Adam works out every 8 days and Susan works out every 12 days. If both Adam and Susan work out today, how many days until they work out on the same day again?

### Clarifications

Clarification 1: Within this benchmark, expectations include finding greatest common factor within 1,000 and least common multiple with factors to 25.

Clarification 2: Instruction includes finding the greatest common factor of the numerator and denominator of a fraction to simplify a fraction.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Number Sense and Operations
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.NSO.3.AP.1: Use tools to find the greatest common factor and least common multiple of two whole numbers 50 or less.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Least Common Multiples:

Students are asked to find the least common multiple of 8 and 12 and to explain how they found their answers.

Type: Formative Assessment

Greatest Common Factors:

Students are given two whole numbers less than or equal to 100 and asked to find the greatest common factor.

Type: Formative Assessment

## Original Student Tutorials

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

## Tutorials

Least Common Multiple:

This video demonstrates the prime factorization method to find the lcm (least common multiple).

Type: Tutorial

Least Common Denominators:

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases.  Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion.  This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.

Type: Tutorial

## Video/Audio/Animation

LCM and GCF Word Problems:

Here we have a couple of word problems searching for the least common multiple and the other for the greatest common factor.

Type: Video/Audio/Animation

## MFAS Formative Assessments

Greatest Common Factors:

Students are given two whole numbers less than or equal to 100 and asked to find the greatest common factor.

Least Common Multiples:

Students are asked to find the least common multiple of 8 and 12 and to explain how they found their answers.

## Original Student Tutorials Mathematics - Grades 6-8

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

## Tutorials

Least Common Multiple:

This video demonstrates the prime factorization method to find the lcm (least common multiple).

Type: Tutorial

Least Common Denominators:

In this tutorial, students will be exposed to the strategy of finding the least common denominator for certain cases.  Elementary teachers should note this is not a requirement for elementary standards and consider whether this video will further student knowledge or create confusion.  This chapter explains how to find the smallest possible common denominator. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.