LCM of 6, 9 and 12
The LCM of 6, 9 and 12 is 36.
Method 1: list the multiples until one matches
| Multiples of | … |
|---|---|
| 6 | 6, 12, 18, 24, 30, 36, 42, … |
| 9 | 9, 18, 27, 36, 45, 54, 63, … |
| 12 | 12, 24, 36, 48, 60, 72, 84, … |
The first multiple on every list is 36.
Method 2: prime factorisation
6 = 2 × 3
9 = 32
12 = 22 × 3
Take every prime that appears in any of them, with its highest power: 22 × 32 = 36.
Method 3: the division (ladder) method
| Divide by | Row |
|---|---|
| 2 | 6 · 9 · 12 |
| 2 | 3 · 9 · 6 |
| 3 | 3 · 9 · 3 |
| 3 | 1 · 3 · 1 |
| 1 · 1 · 1 |
Divide the row by a prime that goes into at least one number, bringing the others down unchanged, until every entry is 1. Multiply the divisors: 2 × 2 × 3 × 3 = 36.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the LCM of 6 and 10.
Answer: 30
2. Find the LCM of 12 and 9.
Answer: 36
3. Add 1/6 + 1/9 (common denominator).
Answer: 10/36
4. Find the GCF of 6 and 9.
Answer: 3
5. Two lights flash every 6 s and 9 s; when do they flash together?
Answer: every 36 s
📚 The class this belongs to
The LCM is taught in Grade 5 and 6 in the US (Common Core 6.NS.4), Year 6 and 7 in the UK, Class 5 and 6 in CBSE and Year 6 and 7 in Australia, usually together with the HCF or GCF.
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