Download Activity 1 – Least Common Multiple

Getting Reading for Algebra by Using Virtual Manipulatives
“Finding Least Common Multiples”
SREB Readiness Indicator Addressed: Determine greatest common factor, least common
multiple, and prime factorization of numbers (SREB Indicator #3).
Activity Rationale: In order for students to manipulate terms in algebraic expressions and
equations, determine factors, and simplify equations, they need to understand whole numbers as
products of factors. Through the use of 100s charts and other arrays of numbers students can develop
recognition of patterns, and find multiples and primes that assist in determining greatest common
factor and least common multiple.
The online applet used in this activity is based on the work of the early mathematician, Eratosthenes
of Cyrene (276-194 BC), who invented a method for efficiently constructing tables of prime
numbers. He devised a “sieve” to identify prime numbers. This sieve, now referred to as the Sieve of
Eratosthenes, drains out composite numbers and leaves prime numbers behind.
The online applet incorporates Eratosthenes’ sieve for positive integers through 200 and has
incorporated features that also show multiples. This tool allows users to explore numeric patterns of
prime and composite numbers. (The number is prime if it has exactly two positive divisors --- 1 and
itself. Otherwise it is composite. The number 1 is usually regarded as being neither prime nor
composite.)
Experience It!
1. Go to http://matti.usu.edu/nlvm/nav/frames_asid_158_g_3_t_1.html?open=instructions.
The Sieve of Eratosthenes applet displays a grid containing numbers from 2 to 200. You can use
it to explore patterns and relationships involving multiples.
2. Click the Show Multiples button.
The applet will display the multiples of the number that you select in the next step.
3. Click 5.
All the multiples of 5 that are between 2 and 200 become highlighted in red. Drag the scrollbar
on the right edge of the workspace to scroll up or down.
4. Describe the pattern that is created.
5. Click the Reset button.
© 2000-2006 Education Development Center, Inc., through its project, EdTech Leaders® Online,
http://www.edtechleaders.org . All rights reserved.
6. Click 2.
All the multiples of 2 that are between 2 and 200 become highlighted in blue. Drag the scrollbar
on the right edge of the workspace to scroll up or down.
7. Describe the pattern that is created.
8. Click the Reset button.
9. Now let’s compare the multiples of 5 and 2. Click 5 followed by the number 2.
Note: When you want to display the multiples of two different numbers, always enter the largest
number followed by the smallest.
You will notice the multiples of 5 and 2 are designated by different colors.
Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40…
Multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20…
The numbers 10, 20, 30, …, 100, and so on, are multiples of both 5 and 2. (On the chart, they are
highlighted in red and blue.) These are called common multiples. The common multiple that is
the smallest in value is called the Least Common Multiple or LCM.
10. What is the Least Common Multiple (LCM) of 5 and 2? How do you know?
Additional Activity: Investigate the Factor Tree virtual manipulative
(http://matti.usu.edu/nlvm/nav/frames_asid_202_g_3_t_2.html) to determine the Least Common
Multiples and Greatest Common Factors of different sets of numbers.
© 2000-2006 Education Development Center, Inc., through its project, EdTech Leaders® Online,
http://www.edtechleaders.org . All rights reserved.
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