Least Common Multiple
Smallest positive number that is a multiple of both numbers.
Key idea
Smallest positive number that is a multiple of both numbers.
In depth
The LCM is the smallest number that both numbers divide into. It is needed to add fractions with different denominators. From prime factorizations, take every prime at its largest power.
Worked example
LCM(4, 6): 4 = 2², 6 = 2×3, so LCM = 2²×3 = 12.
Formula
Real-world uses
- Finding when two repeating events line up, such as traffic lights
- Adding fractions with different denominators
Common mistake
Multiplying the numbers and not dividing out common factors, giving a common multiple that is not the smallest.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Least Common Multiple?
Smallest positive number that is a multiple of both numbers. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Least Common Multiple?
The key formula is lcm(a,b) = a·b / gcd(a,b).
Where is Least Common Multiple used in real life?
Real-world examples: Finding when two repeating events line up, such as traffic lights; Adding fractions with different denominators.
What should I learn before Least Common Multiple?
Make sure you are comfortable with Greatest Common Divisor, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Least Common Multiple?
Multiplying the numbers and not dividing out common factors, giving a common multiple that is not the smallest.
How can I practise Least Common Multiple?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Least Common Multiple?
Move on to Euclidean Algorithm next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.