Least common multiple
The LCM is the smallest positive integer divisible by every number entered. It is especially useful when adding fractions with different denominators.
LCM and GCF Calculator
Last updated: April 2026
Numbers
Least common multiple
LCM(12, 18) = 36
Step-by-step working
- GCF(12, 18) = 6
- LCM(a, b) = (a x b) / GCF(a, b)
- LCM = (12 x 18) / 6 = 36
- 12 = 2^2 x 3
- 18 = 2 x 3^2
- Highest powers: 2^2 x 3^2
Verification
36 / 12 = 3 OK
36 / 18 = 2 OK
Prime factorisation display
Division method for 12
12 / 2 = 6 6 / 2 = 3 3 / 3 = 1
Division method for 18
18 / 2 = 9 9 / 3 = 3 3 / 3 = 1
What is LCM and when is it used?
LCM is used when you need a shared multiple, such as finding a common denominator before adding or subtracting fractions.
GCF/GCD explained
GCF is the biggest factor shared by all numbers. It helps simplify fractions and divide quantities into equal groups.
Euclidean algorithm
The Euclidean algorithm repeatedly divides and keeps the remainder. When the remainder reaches zero, the last non-zero remainder is the GCF.
LCM and GCF in fraction arithmetic
LCM gives the lowest common denominator. GCF helps reduce the final answer to its simplest form.
What does this mean?
This calculator is designed to help you understand the likely number before you make a decision or start an application.
Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.
Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.
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