LCM Calculator
Compute the least common multiple: LCM(A, B) = |A × B| ÷ GCF(A, B).
Calculator
Use the LCM Calculator
Result
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Formula
LCM(A, B) = |A × B| ÷ GCF(A, B)
Step-by-step
- 1
Enter integers
Provide the two integer values.
- 2
Compute LCM
Divide the product by the GCF.
Worked example
Example input: a: 4, b: 6
Result: 12
Related tools
- GCF Calculator
Greatest common factor.
- Prime Factorization
List prime factors to compute the LCM.
Frequently asked questions
How do you calculate the LCM by hand?
Find the GCF of A and B first, then multiply A and B and divide by the GCF. For example, LCM(4, 6) = (4 × 6) ÷ 2 = 12.
What is the LCM of 4 and 6?
12 is the least common multiple: multiples of 4 are 4, 8, 12, … and multiples of 6 are 6, 12, …, so 12 is the smallest number that appears in both lists.
When is the LCM useful?
The LCM is used to add fractions with different denominators, align repeating schedules, and solve problems where two cycles meet, such as buses leaving every 4 and 6 minutes.
Do the two inputs have to be integers?
Yes. Least common multiple is defined for whole numbers, so this calculator expects integers. Enter both values without decimal points.
What is the LCM of 6 and 8?
24. The multiples of 6 are 6, 12, 18, 24, … and the multiples of 8 are 8, 16, 24, …, so 24 is the smallest number appearing in both lists. The formula agrees: (6 × 8) ÷ GCF(6, 8) = 48 ÷ 2 = 24.
How do you find the LCM by listing multiples?
Write out the multiples of each number in increasing order, then circle the first number that appears in every list — that circled value is the LCM. For example, lists for 9 (9, 18, 27, 36, 45) and 12 (12, 24, 36) first share 36, so LCM(9, 12) = 36.
What does LCM stand for?
Least Common Multiple — the smallest positive integer that all of the given numbers divide into evenly. It is also called the lowest common multiple when fractions use it as their common denominator.
What is the LCM of 8 and 12?
24. The multiples of 8 run 8, 16, 24, 32, … and the multiples of 12 run 12, 24, …, so 24 is the first value both lists share. The formula agrees: LCM(8, 12) = (8 × 12) ÷ GCF(8, 12) = 96 ÷ 4 = 24.
What is the LCM of 9 and 12?
36. The 9-list runs 9, 18, 27, 36 and the 12-list runs 12, 24, 36 — both lists first meet at 36. Formula check: LCM(9, 12) = (9 × 12) ÷ GCF(9, 12) = 108 ÷ 3 = 36.
What is the LCM of 12 and 18?
36. Multiples of 12 are 12, 24, 36, … and multiples of 18 are 18, 36, …, so the smallest number appearing in both lists is 36. By the formula: LCM(12, 18) = (12 × 18) ÷ GCF(12, 18) = 216 ÷ 6 = 36.
What is the LCM of 16 and 24?
48. The multiples of 16 go 16, 32, 48 and the multiples of 24 go 24, 48, so 48 is the least common multiple. Formula check: LCM(16, 24) = (16 × 24) ÷ GCF(16, 24) = 384 ÷ 8 = 48.
What is the LCM of 15 and 20?
60. Fifteen climbs by fifteens (15, 30, 45, 60) and twenty by twenties (20, 40, 60) — the first meeting point is 60. By the formula: LCM(15, 20) = (15 × 20) ÷ GCF(15, 20) = 300 ÷ 5 = 60.
What is the LCM of 10 and 15?
30. Multiples of 10 are 10, 20, 30 and multiples of 15 are 15, 30, so the least common multiple is 30. Formula check: LCM(10, 15) = (10 × 15) ÷ GCF(10, 15) = 150 ÷ 5 = 30.
How do you find the LCM using prime factorization?
Factor each number into primes, then take every prime at its highest power: 16 = 2⁴ and 24 = 2³ × 3, so the LCM carries 2⁴ and 3 and lands on 48. The GCF run of the same method works in reverse — shared primes at their lowest power, here 2³ = 8 — which is why LCM × GCF always rebuilds the product 16 × 24.