Finding the LCM
Brian Roska
EdTech 506-4172
Dr. Yu-Chang Hsu
Summer 2012
Lesson Title: Finding the LCM
Grade Level / Subject Area: 6th Grade Mathematics
Time allotted for the lesson: 1 class period or 60-90 minutes
Lesson Description:
This lesson involves two siblings who get on two different-sized Ferris wheels at the same time. After
what number of revolutions of the two wheels will the two siblings both arrive at the bottom? This is an
application of common multiples. If we ask for the first revolution in which this happens, we are finding
the least common multiple.
Core Standards met in this lesson:
This lesson covers the following Number System Standard for 6th grade as set forth by the Common Core
State Standards for Mathematics:
Compute fluently with multi-digit numbers and find common factors and multiples.
•
•
6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and
the least common multiple of two whole numbers less than or equal to 12. Use the distributive
property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a
sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
Instructional Objectives:
• Recognize situations in which finding common factors of whole numbers is important.
• Develop strategies for finding common multiples.
• Observe patterns in common multiples of numbers and use the patterns to reason about and
predict future occurrences and solve problems.
Instructional Procedures:
Lesson Launch: The lesson will start with a small discussion about how multiples are the product
of two whole numbers. Then ask students to think about a few questions. What are the first ten
multiples of 20 and 30? What numbers occur on both lists? The numbers that occur on both lists
are called common multiples. What is the least number that occurs on both lists? This number is
the least common multiple. When the students are observed to have a good idea of what
common multiples are move on to the lesson.
Techniques and activities:
• Begin with direct instruction asking if students have ever seen or ridden on a Ferris
wheel. Explain that there is a place that has two Ferris wheels right next to one another.
Two people can get on them, but
they are different sizes. In one
example Andrew and his sister
Sarah get on the two different
sized Ferris wheels. Andrew
reaches the bottom every 60
seconds while Sarah reaches the
bottom every 40 seconds. If they
are both at the bottom now, how
many seconds will it be until they
are both at the bottom at the same
time? Discuss that the students are
using the multiples of each number
to find the next time they are at
the bottom together or the LCM.
• Allow time for Guided Practice as the students work on a few practice examples either
alone or in pairs. (Remember, anytime kids are talking about Math it is a good thing! Do
not discourage kids from working things out together!) Check informally for
understanding.
Lesson Closure: The students will complete this lesson with activity questions to be completed
either independently or in pairs. The questions worked on will be checked as a class at the beginning
of the next class period.
Adaptations for special learners: Adaptations will be made for those learners needing
accommodations per an IEP or 504. Any remediation needed will be aided by calculators,
multiplication charts or peer tutoring.
Supplemental Activities: Extension and remediation is accomplished using peer tutoring during
the class time as students work with one another. If students are paired in the classroom effectively,
the students who need assistance are provided remediation from those students who benefit from
extension activities. Students who need more significant activities will be dealt with on a one to one
basis with the instructor.
Assessment/Evaluation: Students will be working on the following questions:
Andrew and his little sister, Sarah, are at a carnival. There are both a large and a small Ferris
wheel. Andrew gets on the large Ferris wheel at the same time his sister gets on the small
Ferris wheel. The rides begin at the same time. For each situation below, decide how many
seconds will pass before Andrew and Sarah are both at the bottom again.
 The large wheel makes one revolution in 60 seconds and the small wheel makes one
revolution in 20 seconds.
 The large wheel makes one revolution in 50 seconds and the small wheel makes one
revolution in 30 seconds.
 The large wheel makes one revolution in 10 seconds and the small wheel makes one
revolution in 7 seconds.
For the three questions above, determine the number of times each Ferris wheel goes around
before Andrew and his sister are both on the ground again.
Students will be assessed on this lesson through informal observation, a quiz and the
following 4 point rubric for the problems.
4 pts.
3 pts.
2 pts.
1 pt.
3 questions
correct
2 questions
correct
2 questions
correct
< 1 questions
correct
Learner Products: Students will be completing activity questions from this lesson that will be
recorded in their student notebook.
* Note for learners: This lesson plan template is adapted from the model that is recommended in the
book Preparing to Use Technology: A Practical Guide for Technology Integration.