Lesson plan: using a multiplication table to find least common multiple
The least common multiple, or LCM, is a practical way for students to compare multiples and solve problems involving repeated events. A multiplication table gives learners a familiar visual tool for finding the first number shared by two or more lists of multiples.
This lesson connects multiplication facts, skip counting, factors, and divisibility. It is suitable for upper elementary students who know basic times tables and are beginning to work with common multiples, fractions, or real-world schedules.
The activities move from guided discovery to independent practice. Students first build lists of multiples, then locate the smallest shared value, explain their reasoning, and apply the strategy to word problems.
Learning goals and preparation
By the end of the lesson, students should be able to define a multiple, identify common multiples, and use a multiplication table to find the least common multiple of two numbers. They should also be able to explain why the first shared multiple is the least one.
Prepare a multiplication chart for each student or pair, pencils, highlighters in two colors, and a set of task cards. A whiteboard or document camera will help the teacher model the process. Printable worksheets can provide additional practice for students who need repetition or a record of their work.
Before beginning, review skip counting and multiplication facts. If students need extra fluency support, a short warm-up using finger tricks for the 9 times table can reinforce the connection between multiplication facts and organized number patterns.
Activate prior knowledge
Start by asking students to list the first five multiples of 3. Record 3, 6, 9, 12, and 15, and explain that these numbers are found by multiplying 3 by 1, 2, 3, 4, and 5. Repeat with 4, then invite students to compare both lists.
Students should notice that 12 appears in both lists. Introduce the term common multiple and explain that 12 is the least common multiple because it is the smallest number shared by the two sets. Emphasize that the word least requires students to check the shared values from the beginning rather than choosing any common multiple.
Model the multiplication table strategy
Display a multiplication table and select the numbers 4 and 6. Trace the row or column for 4 and highlight 4, 8, 12, 16, 20, and 24. Use a second color to mark the multiples of 6: 6, 12, 18, and 24. The first number highlighted in both colors is 12, so LCM(4, 6) = 12.
Explain that the table organizes repeated addition into multiplication facts. Students do not need to memorize a special formula for this method; they can search the multiples of each number until they find the first overlap. Ask them to describe why 24 is a common multiple but not the least common multiple.
| Pair of numbers | Multiples of the first number | Multiples of the second number | Least common multiple |
|---|---|---|---|
| 3 and 4 | 3, 6, 9, 12, 15 | 4, 8, 12, 16 | 12 |
| 4 and 6 | 4, 8, 12, 16, 20 | 6, 12, 18, 24 | 12 |
| 5 and 8 | 5, 10, 15, 20, 25, 30, 35, 40 | 8, 16, 24, 32, 40 | 40 |
| 6 and 9 | 6, 12, 18, 24, 30, 36 | 9, 18, 27, 36 | 18 |
Guide collaborative practice
Place students in pairs and give each pair several number cards, such as 2 and 5, 3 and 7, or 8 and 12. One student identifies the multiples of the first number, while the other marks the multiples of the second number. They then switch roles for the next card.
Ask pairs to record the first three common multiples whenever possible. This reinforces the difference between a common multiple and the least common multiple. For example, the common multiples of 4 and 6 include 12, 24, and 36, but only 12 is the least.
Circulate and listen for common errors. Some students may choose the largest highlighted number, while others may confuse factors with multiples. Prompt them to return to the definitions: factors divide a number evenly, while multiples are products created by multiplying a number by whole numbers.
Apply LCM to everyday situations
Present short problems that make repeated cycles meaningful. For example: “A red light flashes every 4 seconds and a blue light flashes every 6 seconds. If both flash now, after how many seconds will they flash together again?” Students list multiples of 4 and 6, identify 12, and write a complete sentence.
Additional contexts can include bells ringing, buses arriving, exercise routines, or classroom jobs repeating on different schedules. Encourage students to underline the repeating intervals and explain why the first shared time represents the least common multiple.
For students ready for an extension, provide three numbers, such as 3, 4, and 6. Students can mark all three sets of multiples on a chart and find the first value shared by every set. This prepares them for more advanced work with equivalent fractions and common denominators.
Recommendations for differentiation
- Provide a partially completed multiplication chart for students who need visual or organizational support.
- Let learners use skip-counting strips, counters, or colored overlays before moving to independent chart work.
- Challenge confident students to compare the table method with prime factorization and explain when each method is efficient.
- Pair students strategically so they can discuss why a number is common and why it is least.
- Use an exit ticket with one computation problem and one explanation prompt.
Check understanding and follow up
For assessment, give students two pairs of numbers and one short word problem. A successful response should show accurate multiples, identify the first shared value, and explain the reasoning in words or a labeled chart. Check whether students understand the vocabulary as well as the procedure.
An exit ticket might ask students to find the LCM of 5 and 10 and explain why 10 is the answer. Another prompt could ask them to correct the statement, “20 is the LCM of 4 and 5,” by showing that 20 is common but that 20 is actually the first shared multiple in this case—helping students distinguish correct reasoning from unsupported guesses.
Keep completed charts and worksheets for a later lesson on equivalent fractions. The same skill will help students find common denominators, compare fractional quantities, and recognize patterns in multiplication. Revisit the activity with new number pairs until students can move from visual marking to efficient mental reasoning.
Print a multiplication chart, select a few accessible number pairs, and guide students through the highlighting process today. With repeated practice, learners can turn a familiar times table into a reliable tool for solving least common multiple problems.