LCM of 4 and 30
The LCM of 4 and 30 is 60. The GCF (HCF) is 2.
Method 1: list the multiples until one matches
| Multiples of | … |
|---|---|
| 4 | 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, … |
| 30 | 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, … |
The first multiple on every list is 60.
Method 2: prime factorisation
4 = 22
30 = 2 × 3 × 5
Take every prime that appears in any of them, with its highest power: 22 × 3 × 5 = 60.
Method 3: the division (ladder) method
| Divide by | Row |
|---|---|
| 2 | 4 · 30 |
| 2 | 2 · 15 |
| 3 | 1 · 15 |
| 5 | 1 · 5 |
| 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 × 5 = 60.
Method 4: LCM = product ÷ GCF
GCF of 4 and 30 = 2, so LCM = 4 × 30 ÷ 2 = 120 ÷ 2 = 60.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the LCM of 4 and 31.
Answer: 124
2. Find the LCM of 8 and 30.
Answer: 120
3. Add 1/4 + 1/30 (common denominator).
Answer: 17/60
4. Find the GCF of 4 and 30.
Answer: 2
5. Two lights flash every 4 s and 30 s; when do they flash together?
Answer: every 60 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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