LCM of 15 and 16
The LCM of 15 and 16 is 240. The GCF (HCF) is 1.
Method 1: list the multiples until one matches
| Multiples of | … |
|---|---|
| 15 | 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, … |
| 16 | 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, … |
The first multiple on every list is 240.
Method 2: prime factorisation
15 = 3 × 5
16 = 24
Take every prime that appears in any of them, with its highest power: 24 × 3 × 5 = 240.
Method 3: the division (ladder) method
| Divide by | Row |
|---|---|
| 2 | 15 · 16 |
| 2 | 15 · 8 |
| 2 | 15 · 4 |
| 2 | 15 · 2 |
| 3 | 15 · 1 |
| 5 | 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 × 2 × 2 × 2 × 3 × 5 = 240.
Method 4: LCM = product ÷ GCF
GCF of 15 and 16 = 1, so LCM = 15 × 16 ÷ 1 = 240 ÷ 1 = 240.
🧮 Calculator
The answer appears here, with the working in words.
✏️ Five questions, answers hidden
1. Find the LCM of 15 and 17.
Answer: 255
2. Find the LCM of 30 and 16.
Answer: 240
3. Add 1/15 + 1/16 (common denominator).
Answer: 31/240
4. Find the GCF of 15 and 16.
Answer: 1
5. Two lights flash every 15 s and 16 s; when do they flash together?
Answer: every 240 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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