LCM of 2, 3 and 5
The LCM of 2, 3 and 5 is 30.
Method 1: list the multiples until one matches
| Multiples of | … |
|---|---|
| 2 | 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, … |
| 3 | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, … |
| 5 | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, … |
The first multiple on every list is 30.
Method 2: prime factorisation
2 = 2
3 = 3
5 = 5
Take every prime that appears in any of them, with its highest power: 2 × 3 × 5 = 30.
Method 3: the division (ladder) method
| Divide by | Row |
|---|---|
| 2 | 2 · 3 · 5 |
| 3 | 1 · 3 · 5 |
| 5 | 1 · 1 · 5 |
| 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 × 3 × 5 = 30.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the LCM of 2 and 4.
Answer: 4
2. Find the LCM of 4 and 3.
Answer: 12
3. Add 1/2 + 1/3 (common denominator).
Answer: 25/30
4. Find the GCF of 2 and 3.
Answer: 1
5. Two lights flash every 2 s and 3 s; when do they flash together?
Answer: every 30 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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