LCM Calculator

LCM and GCF Are a Pair

If you’ve used the GCF Calculator on this site, LCM is its natural counterpart. GCF finds the largest number that divides evenly into a set of numbers; LCM finds the smallest number that a set of numbers all divide evenly into. One shrinks toward the numbers, the other grows away from them.

They’re connected by a clean formula for any two numbers a and b: LCM(a, b) × GCF(a, b) = a × b. The calculator above checks this relationship automatically whenever you enter exactly two numbers.

Worked Example — LCM(8, 12)

Step 1. Prime factorize each number: 8 = 2³, and 12 = 2² × 3.

Step 2. For every prime that shows up in either factorization, take the highest power it appears with: 2 shows up as 2³ (from 8) and 2² (from 12) — take 2³. 3 only shows up as 3¹ (from 12) — take 3¹.

Step 3. Multiply: 2³ × 3 = 8 × 3 = 24.

Check it: 24 ÷ 8 = 3 exactly, and 24 ÷ 12 = 2 exactly — 24 is the smallest number both divide into cleanly.

Common Mistakes

• Confusing LCM with GCF. GCF(8, 12) = 4 (the largest shared factor); LCM(8, 12) = 24 (the smallest shared multiple). They’re opposite operations, and it’s easy to answer the wrong one under time pressure.
• Taking the lowest power of a shared prime instead of the highest. For LCM you always want the highest power that appears anywhere in the list, not the smallest.
• Just multiplying all the numbers together. That gives a common multiple, but not usually the least one — it skips canceling out primes the numbers already share.
• Forgetting a number is already prime. If one of your numbers is a prime like 17, its factorization is just itself to the first power — there’s nothing more to break down.