The same two lists, read the other way
Take 12 = 2 × 2 × 3 and 18 = 2 × 3 × 3. What is their LCM?
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Step 1 of 4
- 12 = 2 × 2 × 3.
- 18 = 2 × 3 × 3.
- Take the most of each piece: two 2s, two 3s.
- Pool: 2 × 2 × 3 × 3 = 36.
Keep everything, take the most of each
The LCM of 12 and 18 is 36.
To pool two lists is to put them together. Pool both prime lists. Keep the most of each prime. Multiply the pool. That is the LCM.
For the prime 2, 12 has two 2s and 18 has one. Keep two 2s. For the prime 3, 12 has one 3 and 18 has two. Keep two 3s.
LCM(12, 18) = 36.
Check: 2 × 2 × 3 × 3 = 4 × 9 = 36.
Two numbers may share no prime. Then the pool has every prime from both. So LCM(8, 15) = 8 × 15 = 120.
Watch out!
Multiplying 12 × 18 gives 216. That is six times the real LCM, 36.