Download Number 2 - GCF LCM_1

Math 10C
Real Numbers: Lesson #2
Applications of Prime Factors: Part 1
GCF and LCM
Objective: By the end of this lesson, you will be able to:
- Determine the greatest common factor and least common multiple of a set of whole
numbers
- Solve problems that involve GCF and LCM
Warm-Up:
 Consider the numbers 48 and 72.
i) List all the factors of each number.
ii) What factors do both numbers have in common?
iii) List the first six multiples of each number.
iv) Which multiples do both numbers have in common?
Definition:
 Greatest Common Factor (GCF) –
e.g. 1) Use your work above to state the greatest common factor of 48 and 72.
In the above example, it was fairly easy to find the GCF because the numbers are relatively small
and don’t have very many factors. With larger numbers that have more factors, it may be easier
to use prime factorization to find the GCF, as shown below.
Math 10C
Real Numbers: Lesson #2
We will work through the steps to find the GCF of 198 and 270.
Steps:
1. Find the prime factorization of each number.
2. Circle the factors that appear in ______ the prime factorizations.
3. _____________ these numbers together (just 1 of each). This is the GCF.
e.g. 2) Use prime factorization to determine the greatest common factor of 285, 399, and 1140.
Definition:
 Least Common Multiple (LCM) –
There are a number of methods to find the LCM.
Method 1:
Make a list of the first several multiples of each number until you find the lowest one that is
common to both lists. This is the method we used in the Warm-Up.
e.g. 3) Use your lists from the Warm-Up to find the least common multiple of 48 and 72.
Math 10C
Real Numbers: Lesson #2
Method 2:
Make a list of the multiples of the ______________ number, and then check whether each is a
multiple of the other number(s).
e.g. 4) Find the least common multiple of 18, 20, and 30.
Method 3:
Use prime factorization, as shown below.
We will work through the steps to find the LCM of 135, 45, and 63.
Steps:
1. Find the prime factorization of each number.
2. Circle the _______________ power of each prime factor in any list.
3. ______________ these numbers together (with their exponents). This is the LCM.
For the last two examples, you will have to figure out whether you need to use the GCF or the
LCM to solve each problem.
e.g. 5) Hamburger patties come in packages of 10. Buns come in packages of 12. What is the
least number of hamburgers that can be made with no patties or buns left over?
Math 10C
Real Numbers: Lesson #2
e.g. 6) Kim wants to tile a rectangular room with square tiles. The room has dimensions 28 feet
by 40 feet.
a) What is the side length of the largest square tile she can use if she does not want to
have to cut the tiles?
b) How many tiles would she need?
Assignment:
p. 140-141 #8-9, 11-13, 17-18, 19a
For a challenge: #14-16