Least Common Multiples

Least Common Multiples

Finding least common multiples is a preliminary step in adding and subtracting fractions with unlike denominators. It is also the strategy used to solve problems when two unequal quantities need to match up. For example, suppose you have two wheels of two different sizes or circumferences. If you make a mark at the bottom of each wheel and then start rotating the wheels, when will points on the two wheels come into sync or align again?

Spreadsheets are another way of helping students see how common multiples can be found by generating a series of numbers and then finding the first common number. This is particularly helpful if you are using more than two numbers. Spreadsheets are another way of examining series or patterns of numbers. These exercises can also be useful in relating common multiples to adding or subtracting fractions with unlike denominators.

Math Objective	To show students how least common multiples are achieved using two and three numbers.
Skills/Outcomes	Using a formula with a constant Filling a formula across a row

Files to Use

Download Info/Instructions

lcm.doc

lcm.xls

Optional Resources

calculators

Classroom Discussion and Activities

Computer Lab Activities

Classroom Discussion and Activities

Teacher Note: This activity should not replace traditional paper and pencil methods for finding common multiples, especially for the numbers frequently found in denominators of fractions.

When the purpose of teaching common multiples is to find the least common multiple for fractions, the numbers used should stay within the range of fractions encountered in normal life. Students should then be working with denominators of 2, 3, 4, 5, 6, 8, 16, 12, and 10.

It may be helpful to have students organize their searches for common multiples on a grid such as the one below. The top number is the factor used to multiply the numbers in the problems. An example of this kind of student worksheet is available in lcm.doc.

Find the least common multiple for 6 and 15.

This grid will provide a natural transition to the spreadsheet activity. You can use calculators to have students complete exercises like the one above. Just multiply row and column numbers (e.g., 6 x 2, 6 x 3) and fill in the grid. The next step is to look back over the series and find the common number. In this case, it would be 30. This practice provides a foundation for common multiples.

To prepare the computer activity, give students a blank spreadsheet grid. These can be found in grid wksht. Have them write the formula in cells B2 and B3 as shown below, using the numbers in the problem (in this case, 6 and 15) as the constants. Tell them that in the lab, they will use the FILL RIGHT command to copy the formula over as many places as needed. You may want students to write this command in the cells to the right of the formulas so that they remember.

Computer Lab Activities

Teacher Note: Here's a formatting tip. It is helpful to use colors and borders to help keep the different multiples separate from the factors. We have set up some sample exercises like this in lcm.xls.

Enter the problems from their paper lab sheet into a new Excel file.

Set up the numbers across the top and the bordered cells below. Or, use the examples in lcm.xls and clear the contents (EDIT- CLEAR - CONTENT commands).

Once students have set up the first formula, use the FILL RIGHT command.

Have students search for the least common multiples or all the common multiples.

Give them additional sets of numbers, including 3 or 4 numbers at a time, to extend this concept of common multiples.

Added Exercises

Let the students submit 2 or 3 numbers for their common multiple problems.

Use story problems as a context for these exercises, especially if you are doing consumer math.

Build basic sets for numbers which are frequently used as denominators in adding and subtracting fractions. For example, 4, 12 or 6, 8 or 5, 7. Print out the strips and mount to index cards. These can be used for reference when students work with fractions.