Least Common Multiple Calculator
Find the LCM of several numbers, with the prime factorization behind it.
About Least Common Multiple Calculator
The Least Common Multiple of a set of numbers is the smallest positive integer that is a multiple of every number in the set. It's calculated as lcm(a, b) = (a × b) / gcd(a, b), where gcd is the Greatest Common Factor. For a list, fold pairwise: lcm(a, b, c) = lcm(lcm(a, b), c). The LCM is the key to finding a common denominator when adding fractions.
Formulas
LCM via GCF
lcm(a, b) = |a × b| / gcd(a, b)
- a
- First number
- b
- Second number
LCM of a list (folding)
lcm(a, b, c) = lcm(lcm(a, b), c)
Worked example
With the default values below, Least Common Multiple Calculator returns Least Common Multiple (LCM) of 12. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Numbers (comma or space separated)
- 4, 6
Results
- Least Common Multiple (LCM)
- 12
- Input Numbers
- 4, 6
Step by step
- 1Inputs= 4, 6
- 2GCF(4, 6)= 2
- 3LCM(4, 6)= 12
- 4Verification
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the LCM of 4 and 6?
gcd(4, 6) = 2. LCM = 4 × 6 / 2 = 24 / 2 = 12. Verify: 12 ÷ 4 = 3 ✓ and 12 ÷ 6 = 2 ✓. The LCM of 4 and 6 is 12.
What is the LCM used for in fractions?
To add or subtract fractions with different denominators, you need a common denominator. The Least Common Denominator (LCD) is the LCM of the denominators. For ½ + ⅓: LCD = lcm(2, 3) = 6, giving 3/6 + 2/6 = 5/6.
Is LCM(a, b) × GCF(a, b) = a × b always true?
Yes, for positive integers: lcm(a, b) × gcd(a, b) = a × b. This identity is the basis of the efficient calculation. For example, lcm(4, 6) × gcd(4, 6) = 12 × 2 = 24 = 4 × 6.