What does it mean?
A multiple is the result of taking a whole-number count of equal groups. The common multiples of two positive whole numbers belong to both lists. The lowest common multiple, or LCM, is the smallest positive one. Zero is in both lists too, but it is not the positive meeting point we mean by the LCM.
List the multiples of each number. The first shared multiple is the least common multiple. Use it to find a shared event, not to add fractions yet.
Learning goal: Common multiples and LCM. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Grade 6 Prime Time: factors, multiples and prime numbers if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
List the positive multiples in order and compare the lists. For larger numbers, use prime factors: include each prime the greatest number of times it appears in either factorisation. For 12 = 2² × 3 and 18 = 2 × 3², the LCM is 2² × 3² = 36. Both original numbers divide 36 exactly.
Notation: LCM = least common multiple
Key rule and when to use it
The LCM is the smallest positive multiple shared by the numbers. It is not always their product: LCM(6, 18) = 18.
Worked examples, step by step
Example 1: Find the LCM of 4 and 6.
- Multiples of 4: 4, 8, 12, …
- Multiples of 6: 6, 12, …
- The first shared multiple is 12.
Answer: 12
Example 2: Two lights flash together now, then repeat every 8 seconds and 12 seconds. After how many seconds do they next flash together?
- List multiples of 8.
- List multiples of 12.
- Choose the first number in both lists.
Answer: 24 seconds
Example 3: Two lights flash together now, then repeat every 6 and 9 seconds. When is their next joint flash?
- Multiples of 6 begin 6, 12, 18, 24. Multiples of 9 begin 9, 18, 27.
- The first positive common multiple is 18.
- They flash together again in 18 seconds. Check 18 ÷ 6 = 3 intervals and 18 ÷ 9 = 2.
Common mistakes and important boundaries
The LCM is not always the product. If one number divides the other, the larger number is already the LCM: LCM(4, 12) = 12. A repeating-events problem also needs a common starting time. “Every 4 days” and “every 6 days” meet again after 12 days only when both schedules start together.
A point to explain
Adding 4 and 6 does not find the first shared time.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Lowest Common Multiple: Lists, Cycles and Problems — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
LCM of 4 and 10 = ?
Answer and a way to check
20
List the multiples of both numbers and find the first shared one.
LCM of 8 and 12 = ?
Answer and a way to check
24
List the multiples of both numbers and find the first shared one.
Football and tennis both happen today. Football repeats every 4 days and tennis every 6 days. After how many days do they next coincide?
Answer and a way to check
12
List the multiples of both numbers and find the first shared one.
Find the LCM of 3 and 5.
Answer and a way to check
15
Positive multiples first meet at 15: 3 × 5 = 15 and 5 × 3 = 15.
Find the LCM of 6 and 18.
Answer and a way to check
18
18 is already a multiple of 6 and of 18. A common multiple cannot be smaller than the larger positive input here.
Is zero the LCM of 4 and 6? Explain.
Answer and a way to check
No; the LCM is 12.
LCM means the least positive common multiple. Zero is common but is excluded by that definition.
Bells ring together now, then repeat every 5 and 8 minutes. When do they next ring together?
Answer and a way to check
40 minutes
The first shared positive multiple is 40. Both schedules must have the same starting moment for this conclusion.
Find the LCM of 9 and 12.
Answer and a way to check
36
9, 18, 27, 36 and 12, 24, 36 first meet at 36. Check that both numbers divide it.
Lowest Common Multiple: Lists, Cycles and Problems — answer key
20 List the multiples of both numbers and find the first shared one.
24 List the multiples of both numbers and find the first shared one.
12 List the multiples of both numbers and find the first shared one.
15 Positive multiples first meet at 15: 3 × 5 = 15 and 5 × 3 = 15.
18 18 is already a multiple of 6 and of 18. A common multiple cannot be smaller than the larger positive input here.
No; the LCM is 12. LCM means the least positive common multiple. Zero is common but is excluded by that definition.
40 minutes The first shared positive multiple is 40. Both schedules must have the same starting moment for this conclusion.
36 9, 18, 27, 36 and 12, 24, 36 first meet at 36. Check that both numbers divide it.
Questions students and parents ask
When is multiplying the numbers a quick way to find the LCM?
When the positive integers have no common factor greater than 1. For example, 4 and 9 are coprime, so their LCM is 36. Otherwise list multiples or use prime factors.
How is LCM different from HCF?
The LCM is a common multiple that both original numbers divide into. The HCF is a common factor that divides both original numbers.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Grade 6 Prime Time: factors, multiples and prime numbers. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Use two repeating clap patterns that start together. Count the beats until both patterns land on the same positive beat again.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Common multiples and LCM”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
Need another way to understand it?
Bring one question your child found difficult to a free 50-minute session. Tell us their grade, curriculum and time zone so we can discuss a suitable next step.
Request a free session