LCM Blog: Guides and Practice Sets
Guides on the least common multiple, grouped by what you need. Each one links to the Least Multiple Calculator so you can try the numbers yourself.
| Section | Guides | Start with |
|---|---|---|
| Learn the LCM | 10 | What is the LCM? Definition, full form, examples |
| Methods, step by step | 5 | LCM by prime factorisation |
| Practice and word problems | 2 | LCM questions and worksheets by class / grade |
Learn the LCM
What is the LCM? Definition, full form, examples
The least common multiple defined, with notation, full form and worked examples.
How to find the LCM: methods step by step
Listing multiples, prime factorization, cake, division, GCF and Venn, each worked through.
LCM of fractions and decimals: formula and examples
The LCM of fractions formula, worked examples, and how decimals and mixed numbers are handled.
LCM vs HCF (GCF): difference, formula, when to use which
How the least common multiple and the highest common factor differ and relate.
LCM of Two Numbers in C, C++, Java and Python
Euclid's GCD, then LCM = a ÷ GCD × b: working code in C, C++, Java, Python, C# and JavaScript.
LCM Edge Cases: One Number, Zero, and Negative Numbers
The LCM of one number, why the LCM with 0 is undefined, and how negative numbers are handled.
How to Clear Fractions from an Equation Using the LCM
Multiply every term by the LCM of the denominators: 3 worked examples and the 2 mistakes to avoid.
Multiples of a Number and Common Multiples
Multiples of 1 to 20, how to list common multiples of two or three numbers, and how they lead to the LCM.
Least Common Factor: Why It Is Always 1
The least common factor is always 1; what people usually mean is the LCM or the GCF.
Adding Fractions With Unlike Denominators
Find the LCD, rename, add, simplify: five worked examples, mixed numbers and subtraction.
Methods, step by step
LCM by prime factorisation
The prime factorization method for the LCM, step by step.
LCM by the division (ladder) method
The division and ladder method for the LCM, laid out as a table.
LCM of 3 or more numbers
How to find the LCM of three or more numbers by every method.
LCM of polynomials and algebraic expressions
Factor each polynomial and take every factor at its highest power.
LCM tricks and shortcuts for exams
Fast ways to find the LCM in aptitude and class tests.
Practice and word problems
LCM questions and worksheets by class / grade
Practice sets by class and grade with answers.
LCM word problems and real-life uses
Buses, gears, tiles and fractions: LCM word problems solved.
Frequently asked questions
What is on the LCM blog?
17 guides about the least common multiple: the definition and full form, the six methods, LCM versus HCF, fractions, edge cases, clearing fractions, multiples and word problems.
In what order should I read the guides?
Start with What is the LCM, then How to find the LCM. Pick a method page for the one your class uses, and finish with the practice sets and word problems.
How often are the guides updated?
Each guide shows its published and updated dates under the title. Guides are re-read whenever the calculator code changes and at least once a year.
Sources
- Wikipedia: Least common multiple: definition, notation, LCM × GCD = a × b
- Wolfram MathWorld: Least Common Multiple: formal properties
- Common Core 6.NS.B.4: GCF and LCM in grade 6