 # Least Common Multiple and Greatest Common Factor

Examples, solutions and worksheets to help Grade 6 students learn how to find the least common multiple and greatest common factor and apply factors to the Distributive Property.

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Common Core For Grade 6

### New York State Common Core Math Grade 6, Module 2, Lesson 18

Download worksheets for Grade 6, Module 2, Lesson 18 (Pdf)

### Lesson 18 Student Outcomes

• Students find the least common multiple and greatest common factor and apply factors to the Distributive Property

### NYS Math Module 2 Grade 6 Lesson 18 Classwork

The Greatest Common Factor of two whole numbers a and b, written GCF(a, b), is the greatest whole number, which is a factor of both a and b.
The Least Common Multiple of two nonzero numbers a and b, written LCM(a, b), is the least whole number (larger than zero), which is a multiple of both a and b.

Example 1
Greatest Common Factor: Find the greatest common factor of 12 and 18.
Step 1: Listing these factors as pairs can help you not miss any. Start with one times the number.
Step 2: Circle all factors that appear on both lists.
Step 3: Place a triangle around the greatest of these common factors.

Example 2
Least Common Multiple: Find the least common multiple of 12 and 18.

Exploratory Challenge 1: Factors and GCF
Find the greatest common factor of one of these pairs: 30,50; 30,45; 45,60; 42,70; 96,144.
a. There are 18 girls and 24 boys who want to participate in a Trivia Challenge. If each team must have the same number of girls and boys, what is the greatest number of teams that can enter? How many boys and girls will be on each team?
b. The Ski Club members are preparing identical welcome kits for the new skiers. They have 60 hand warmer packets and 48 foot warmer packets. What is the greatest number of kits they can prepare using all of the hand warmer and foot warmer packets?
c. There are 435 representatives and 100 senators serving in the United States Congress. How many identical groups with the same numbers of representative and senators could be formed from all of Congress, if we want the largest groups possible?
d. Is the GCF of a pair of numbers ever equal to one of the numbers? Explain with an example.
e. Is the GCF of a pair of numbers ever greater than both numbers? Explain with an example.

Exploratory Challenge 2: Multiples and LCM
Find the least common multiple of one of these pairs: 9,12; 8,18; 4,30, 12,30; 20,50
a. Hot dogs come packed 10 in a package. Hot dog buns come packed 8 in a package. If we want one hot dog for each bun for a picnic, with none left over, what is the least amount of each we need to buy?
b. Starting at 6:00 a.m., a bus makes a stop at my street corner every 15 minutes. Also starting at 6:00 a.m., a taxi cab comes by every 12 minutes. What is the next time there will be a bus and a taxi at the corner at the same time?
c. Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has 24 teeth and the second gear has 40 teeth, how many revolutions of the first gear are needed until the marks line up again?
d. Is the LCM of a pair of numbers ever equal to one of the numbers? Explain with an example.
e. Is the LCM of a pair of numbers ever less than both numbers? Explain with an example.

Exploratory Challenge 3: Using Prime Factors to Determine GCF
Factor Tree Game

Exploratory Challenge 4: Applying Factors to the Distributive Property
Find the GCF from the two numbers and rewrite the sum using the Distributive Property How to solve problems using Greatest Common Factors and Least Common Multiples?

Distinguish between GCF and LCM
Example:
Find the GCF and LCM of 8 and 12 Find GCF using the factor tree
GCF and the Distributive Property
Examples:
1. Find the GCF of 48 and 60.
2. Find the GCF 12 and 30 and rewrite their sum using the Distributive Property. LCM, GCF and the Distributive Property
Examples:
1. Find the LCM of 6 and 8. 2. Find the GCF of 48 and 64.
3. Find the GCF 24 and 28 and rewrite their sum using the Distributive Property.

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