How do you solve real world
problems using the Greatest Common
Factor or Least Common Multiple?
Pierce swims every fourth day and
Joshua swims every third day. If
they both swim on the first of the
month, on what date will they both
swim together again?
In this lesson you will learn
when to use the GCF and
LCM to find solutions by
looking at real world
problems.
A Common Misunderstanding
Misreading the problem.
Misinterpreting the solution.
Core Lesson
Close Read the Problem
Pierce swims every fourth day and
Joshua swims every third day. If they
both swim on the first of the month,
on what date will they both swim
together again?
Core Lesson
Organize Information
Swims every
Pierce
Joshua
4 days
3 days
Multiples
{4, 8, 12, 16, 20…}
{3, 6, 9, 12, 15…}
The LCM of 4 and 3 is 12.
answer
statement: The next time Pierce and Joshua swim
together will be on the 12th day of the month.
Core Lesson
When to look for the LCM
• to figure out when two or
more events will happen
again at the same time or
on the same date
• to purchase or get multiple
items of two or more
different things in order to
have enough
• about something that is or
will be happening over
and over
every three days and
every four days
buns in packages of 12
and hot dogs in
packages of 8
every 4 inches and
every 10 inches
Core Lesson
Close Read the Problem
Nhya has 16 girls and 12 boys in his class.
He helps his teacher by making groups
which have the same combination of girls
and boys. What is the largest number of
groups that can be made without leaving
anyone out?
Core Lesson
girls
boys
Organize Information
Class
Factors
16
12
{ 1, 2, 4, 8, 16}
{ 1, 2, 3, 4, 6, 12}
The GCF of 16 and 12 is 4.
answer The largest amount of groups with the
statement: same combination of girls and boys
would be 4.
Core Lesson
When to look for the GCF
• to arrange two or more
things in rows or groups
• to divide things into
smaller sections
• figuring out how many
people can be invited or
receive something
16 girls and 12 boys
8 inch piece of string
and 24 inch piece of
string
20 gumballs and 45
suckers
In this lesson you have
learned when to use the GCF
and LCM to find solutions by
looking at real world
problems.