Multiples
List multiples; nth multiple; count multiples in a range.
Multiples
Multiples of a Number
What you'll learn
- A multiple is the result of multiplying a number by 1, 2, 3, …
- List multiples and find the nth multiple.
- Count multiples in a given range — useful for LCM problems later.
Key concepts
Level 1 — Definition
Multiples of 4: 4, 8, 12, 16, 20, … (4 × 1, 4 × 2, 4 × 3, …)
Verbal: Multiples are times-table answers — they grow by skip counting.
Level 2 — nth multiple
| n | 7 × n | nth multiple of 7 |
|---|---|---|
| 1 | 7 | 7 |
| 5 | 35 | 35 |
| 10 | 70 | 70 |
Rule: nth multiple of a = a × n.
Level 3 — Multiples in a range
Multiples of 6 between 20 and 50: 24, 30, 36, 42, 48 → 5 multiples.
Level 4 — Factor vs multiple (link)
3 is a factor of 12; 12 is a multiple of 3. Same relationship, two views.
Indian context: Auto-rickshaw fare ₹15 per km — distances 15, 30, 45, 60 m are multiples of 15.
NCERT anchor: Math-Magic 4, Ch 11 — Tables and Shares; Ch 10 — Play with Patterns (skip counting on number line)
Worked example
First five multiples of 9
Step 1 — 9×1=9, 9×2=18, 9×3=27, 9×4=36, 9×5=45.
Answer: **9, 18, 27, 36, 45**
How many multiples of 8 lie between 50 and 100?
Step 1 — 8×7=56 (first above 50); 8×8=64; 8×9=72; 8×10=80; 8×11=88; 8×12=96.
Step 2 — 8×13=104 (too big).
Answer: **6 multiples** (56, 64, 72, 80, 88, 96)
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| 0 is not a multiple of 5 | Starting list at first non-zero | 0 = 5×0 — 0 is a multiple of every number |
| Confusing multiple with factor | Reversing the relationship | 15 is a multiple of 3; 3 is a factor of 15 |
| Including numbers that are not exact products | Adding nearby numbers | 14 is not a multiple of 6 (6×2=12, 6×3=18) |
| nth multiple means add n | Using addition instead of × | 8th multiple of 5 = 5×8 = 40, not 5+8 |
Quick check
- Write first six multiples of 7.
- What is the 12th multiple of 4? (48)
- Is 54 a multiple of 9? (yes)
- Stretch: Find the smallest 3-digit multiple of 8. (104)
Revision tip: On a number line, mark multiples of 6 in one colour and multiples of 9 in another — spot where they coincide (LCM preview).
Open the Practice tab for graded questions on Multiples of a Number.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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