What is LCM of 4 and 6?
LCM(4, 6) = 12. Twelve is the smallest number divisible by both 4 and 6.
Least common multiple
LCM = 12
Formula: LCM(a, b) = |a x b| / GCF(a, b)
4 = 2^2
6 = 2 x 3
Find the smallest number divisible by every input—common denominators for fractions, synchronized bus schedules, and gear tooth alignment.
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The LCM of two or more integers is the smallest positive number divisible by every input. LCM(4, 6) = 12—the first time both 4 and 6 land on the same count on a number line.
Least common multiple
LCM = 12
Formula: LCM(a, b) = |a x b| / GCF(a, b)
4 = 2^2
6 = 2 x 3
The least common multiple is the first meeting point on the integer timeline where every input number fits an exact whole number of times.
Consider gears with 8 teeth and 12 teeth. After one full turn of the larger gear, the smaller has made 1.5 turns—they are out of sync. The teeth realign when both have completed a whole number of rotations. That happens at LCM(8, 12) = 24 teeth, meaning 3 turns of the 8-tooth gear and 2 turns of the 12-tooth gear.
For fractions, the LCM of denominators becomes the **lowest common denominator**. Adding 1/4 + 1/6 needs a denominator divisible by both 4 and 6; LCM(4, 6) = 12 gives 3/12 + 2/12 = 5/12.
Prime factorization builds LCM by taking each prime at its **maximum** exponent seen in any input—the opposite rule from GCF, which uses minimum exponents. For two positive integers, LCM(a,b) × GCF(a,b) = |a×b|, linking the two ideas in one identity.
LCM finds the smallest number every input divides evenly—essential for common denominators and repeating-cycle timing.
Concise answers for common searches — definitions, steps, and comparisons.
LCM(4, 6) = 12. Twelve is the smallest number divisible by both 4 and 6.
LCM(a,b) = |a×b| / GCF(a,b). Example: LCM(12,18) = 216/6 = 36.
LCM(3, 5) = 15. Rewrite as 5/15 and 3/15 before adding.
Gears with m and n teeth realign after LCM(m,n) tooth engagements—each gear completes a whole number of turns.
The calculator accepts two or more positive integers, applies prime factorization or the GCF identity LCM(a,b) = |a×b|/GCF(a,b), and chains results for longer lists.
Formula
LCM(a,b) = |a × b| / GCF(a,b). Prime method: LCM = ∏ p_i^max(e_i across inputs). For a list: LCM(a,b,c) = LCM(LCM(a,b), c).Enter every number that must divide the result—e.g. 6, 8, 10 for a three-way cycle or denominators 9 and 12 for fractions.
Optional steps show each prime raised to the highest exponent needed across inputs.
Multiply each fraction's numerator by (LCM ÷ its denominator) so all terms share the new denominator.
Verify LCM(a,b) × GCF(a,b) = a×b for pairs—catches entry typos quickly.
Input
4 and 6Output
LCM = 12Multiples of 4: 4,8,12… Multiples of 6: 6,12… First shared value is 12.
Input
5 and 7Output
LCM = 35No shared factors → product equals LCM. 1/5 + 1/7 uses denominator 35.
Input
6, 8, 10Output
LCM = 120LCM(6,8)=24; LCM(24,10)=120. All three divide 120 evenly.
Input
84 and 126Output
LCM = 252GCF=42. LCM = 84×126/42 = 252.
Input
Denominators 9 and 12Output
LCD = 369=3², 12=2²×3 → LCM = 2²×3² = 36. Scale fractions before adding.
Input
16 and 32Output
LCM = 32Both are powers of 2; take the higher exponent: 2⁵ = 32.
Common real-world scenarios where this tool saves time.
To add 2/9 and 5/12, LCM(9, 12) = 36 becomes the common denominator: 8/36 + 15/36 = 23/36.
Bus A arrives every 15 minutes, Bus B every 20 minutes. They meet at the station every LCM(15, 20) = 60 minutes.
A 14-tooth and 21-tooth gear mesh cleanly every LCM(14, 21) = 42 tooth engagements—useful in maker and engineering sketches.
A 3/4 bar and a 4/4 pulse align on a 12-beat cycle—LCM(3, 4) = 12 underlies polyrhythm math.
Step-by-step chains that connect related tools for common tasks.
| Number | First four multiples | LCM with 6 |
|---|---|---|
| 4 | 4, 8, 12, 16 | 12 |
| 6 | 6, 12, 18, 24 | 12 |
| 5 | 5, 10, 15, 20 | 30 (with 6) |
| 8 | 8, 16, 24, 32 | 24 (with 6) |
| Pair | GCF | LCM | Product check GCF×LCM |
|---|---|---|---|
| 12, 18 | 6 | 36 | 216 = 12×18 |
| 7, 11 | 1 | 77 | 77 = 7×11 |
| 48, 72 | 24 | 144 | 3456 = 48×72 |
GCF × LCM = product for two positive integers.
Prime sketches prevent missing a hidden 2 or 3 that inflates the LCM.
If you already know GCF(a,b), one division gives LCM without listing multiples.
Simplifying 4/8 to 1/2 before hunting LCD keeps numbers smaller—use GCF calculator first.
LCM(a,b,c) = LCM(LCM(a,b), c)—same pattern the tool uses internally.
a×b is usually larger than LCM when numbers share factors. LCM(6,8)=24, not 48.
LCM prime method takes the **highest** power of each prime. GCF uses the lowest—opposite rules.
A common denominator alone is not enough—multiply each top number by (LCD ÷ old denominator).
LCM(6, 10) = 30, which is neither 6 nor 10.
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For fraction denominators, yes—the LCD is the LCM of the denominators after fractions are in lowest terms.
LCM(1, n) = n. One divides everything, so the smallest shared multiple is n itself.
No. The LCM is always at least as large as the biggest number in the set. It equals that number only when it is a multiple of every other input.
LCM(8, 6) = 24. Convert: 9/24 + 4/24 = 13/24.
Listing multiples is slow for large numbers. Prime exponents at max power give LCM directly.
Find LCM of the denominators only—e.g. LCM(4, 6, 9) = 36—then scale each numerator accordingly.
Events repeating every a and b days coincide every LCM(a,b) days—maintenance windows and pill reminders use the same math.
LCM Calculator processes integers locally in your browser without uploading them.
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Reviewed by EverydayTools Editorial Team on 2026-07-03.
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