Least Common Multiple Calculator
Find the least common multiple of two numbers using LCM = a×b ÷ GCF, with the Euclidean algorithm shown in full. A multiples table lists each number’s first multiples side by side so you can see exactly where they coincide.
TheCalculators — Least Common Multiple Calculator
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LCM(12, 18)
36
GCF = 6 · LCM = a×b÷GCF = 216 ÷ 6
- First number
- 12
- Second number
- 18
- LCM
- 36
- GCF used
- 6
- a × b
- 216
- Check: LCM × GCF
- 216 = a × b ✓
- First common multiple of a
- 12 × 3 = 36
First multiples side by side
The smallest value appearing in both columns is the least common multiple.
Step-by-step
- 1Euclid step 112 = 0 × 18 + 12
- 2Euclid step 218 = 1 × 12 + 6
- 3Euclid step 312 = 2 × 6 + 0
- 4GCF foundGCF(12, 18) = 6
- 5Apply the identityLCM = a × b ÷ GCF = 12 × 18 ÷ 6 = 216 ÷ 6 = 36
- 6Verify36 ÷ 12 = 3 and 36 ÷ 18 = 2 — both whole ✓
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Formula
LCM(a, b) = |a × b| ÷ GCF(a, b)
Pro tips
- • The LCM is exactly the lowest common denominator you need when adding fractions like 1/12 + 1/18.
- • Events repeating every a and b units meet again every LCM(a, b) units — buses, planets, blinking lights alike.
- • When GCF is 1 the numbers are coprime and their LCM is simply their product.
FAQ
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