How to Find LCM (Least Common Multiple)

Our LCM calculator takes 2 to 12 whole numbers and uses LCM(a, b) = |a × b| ÷ GCF(a, b), folded pairwise. It does not add the fractions for you — that is the fraction calculator — and it rejects 0 so a classroom LCM stays a positive common multiple.

Paste the integers, separated by commas or spaces. The default 12, 18, 24 should show 72. If the product would not be an exact safe integer, the page errors instead of rounding a huge multiple.

Listing multiples works for small pairs: 12, 24, 36 — 36 is a multiple of 18, so LCM(12, 18) = 36. Prime factors keep the highest exponent of each prime. The GCF identity is fastest on a calculator.

12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. Highest powers: 2³ × 3² = 8 × 9 = 72. Check: 72 ÷ 12 = 6, 72 ÷ 18 = 4, 72 ÷ 24 = 3. No smaller positive integer works.

If the question is “largest number that divides both,” that is GCF, not LCM. 12 and 18 have GCF 6 and LCM 36. For two numbers, GCF × LCM = |a × b|. Use the GCF calculator or the factor calculator when the worksheet says greatest common factor, gcd or hcf.

The least common denominator of 12 and 18 is LCM(12, 18) = 36. Rewrite 1/12 as 3/36 and 1/18 as 2/36, then add: 5/36. That 36 is the number the LCM calculator is for. The fraction calculator will do the rewrite and the simplify in one step; this guide exists because searchers type “lcm calculator” when the worksheet still wants the denominator by itself. Schedules work the same way: a 12-minute bus and an 18-minute bus meet every 36 minutes. Gear teeth, repeating calendar events and “when do these loops line up” are LCM stories, not GCF stories. Paste every period into the LCM calculator, read the common multiple, then go back to the original units — minutes stay minutes; the tool does not convert to hours.