Multiples in Number System & Arithmetic's
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Multiples in Mathematics – Definition, Examples, Properties & 20 MCQs with Detailed Solutions

⭐ MULTIPLES — Detailed Explanation

A multiple of a number is obtained by multiplying the number by any whole number (0, 1, 2, 3…).
In other words:

  • If n = a × k, where k is a whole number, then n is a multiple of a.
  • Example:
    Multiples of 4 → 4, 8, 12, 16, 20…
    (Here 4×1=4, 4×2=8, 4×3=12, etc.)

🧩 Key Characteristics of Multiples

  1. Every number has infinitely many multiples.
  2. The smallest multiple of any number is 0 (because n × 0 = 0).
  3. Every number is a multiple of itself (n × 1 = n).
  4. Even numbers are multiples of 2.
  5. Multiples grow larger than the number except itself.
  6. Common multiples help find LCM.
  7. Multiples are always ≥ the number (except 0).

⭐ 5 Solved Examples of Multiples (With Explanation)

Example 1: List first five multiples of 6

6 × 1 = 6
6 × 2 = 12
6 × 3 = 18
6 × 4 = 24
6 × 5 = 30
✔ First five multiples → 6, 12, 18, 24, 30

Example 2: Is 45 a multiple of 9?

45 ÷ 9 = 5 (exact)
✔ Yes, 45 is a multiple of 9

Example 3: List multiples of 7 less than 40

Multiples: 7, 14, 21, 28, 35
✔ All are < 40.

Example 4: Find common multiples of 4 and 6 less than 50

Multiples of 4: 4,8,12,16,20,24,28,32,36,40,44,48
Multiples of 6: 6,12,18,24,30,36,42,48

Common multiples < 50 → 12, 24, 36, 48

Example 5: Smallest multiple of 15 greater than 100

Multiples of 15: 90,105,120…
First one greater than 100 → 105

MCQ's For Exam

Q.1. Which of the following is a multiple of 3?

  1. 14
  2. 17
  3. 21
  4. 25

3) 21

📝Explanation: 21 ÷ 3 = 7 (exact), so 21 is a multiple of 3. Other numbers do not divide evenly by 3.

Q.2. Which is the smallest multiple of 9?

  1. 0
  2. 9
  3. 18
  4. 27

1) 0

📝 Description: 0 is a multiple of every number because n × 0 = 0.

Q.3. Which of these numbers is NOT a multiple of 4?

  1. 12
  2. 24
  3. 32
  4. 18

4) 18

📝 Description:

18 ÷ 4 is not an integer.
All others divide exactly by 4.

Q.4. The first three multiples of 8 are:

  1. 8, 16, 24
  2. 8, 15, 23
  3. 10, 18, 26
  4. 6, 12, 18

1) 8, 16, 24

📝 Description: Multiples of 8 = 8×1=8, 8×2=16, 8×3=24.

Q.5. Which of the following is a common multiple of 5 and 6?

  1. 20
  2. 25
  3. 30
  4. 35

3) 30

📝 Description: 30 is divisible by both 5 and 6 → 30 ÷ 5=6, 30 ÷6=5.

Q.6. Which number is a multiple of 11?

  1. 44
  2. 38
  3. 27
  4. 56

1) 44

📝 Description: 11 × 4 = 44, so it is a multiple of 11.

Q.7. Which is the smallest multiple of 12 greater than 50?

  1. 48
  2. 60
  3. 72
  4. 84

2) 60

📝 Description:

Multiples: 48,60,72…
First one >50 is 60.

Q.8. Which is a multiple of both 2 and 3?

  1. 9
  2. 11
  3. 12
  4. 21

3) 12

📝 Description:

A number that is a multiple of both 2 and 3 is a multiple of 6.
12 ÷ 6 = 2 → valid.

Q.9. Which number below is a multiple of 7?

  1. 25
  2. 35
  3. 42
  4. Both B & C

4) Both B & C

📝 Description: 

35 = 7×5
42 = 7×6
So both are multiples.

Q.10. Which of these numbers is a multiple of 15?

  1. 22
  2. 45
  3. 50
  4. 72

2) 45

📝 Description: 45 ÷ 15 = 3 → exact.

Q.11. What is the 6th multiple of 9?

  1. 45
  2. 54
  3. 63
  4. 72

3) 63

📝 Description: 

6th multiple = 9 × 6 = 54 (Oops?).
Let’s recheck:
1st=9
2nd=18
3rd=27
4th=36
5th=45
6th=54
Correct answer → 54 (Option B)

Q.12. Which number is NOT a multiple of 10?

  1. 20
  2. 40
  3. 55
  4. 100

3) 55

📝 Description:

Multiples of 10 end in 0.
55 does not.

Q.13. Which number is a multiple of both 4 and 9?

  1. 18
  2. 36
  3. 45
  4. 54

2) 36

📝 Description: 

36 ÷ 4 = 9
36 ÷ 9 = 4
So 36 is a multiple of both.

Q.14. The 3rd multiple of 13 is:

  1. 26
  2. 39
  3. 52
  4. 65

2) 39

📝 Description: 13 × 3 = 39.

Q.15. Which number is a multiple of 16?

  1. 48
  2. 60
  3. 72
  4. 92

1) 48

📝 Description:

48 = 16 × 3 → valid.
Others not divisible by 16.

Q.16. Which is the least common multiple (LCM) of 4 and 5?

  1. 10
  2. 15
  3. 20
  4. 25

3) 20

📝 Description: 

Multiples of 4: 4,8,12,16,20
Multiples of 5: 5,10,15,20
LCM = 20.

Q.17. Which number is a multiple of 18?

  1. 36
  2. 45
  3. 54
  4. Both A & C

4) Both A & C

📝 Description: 

36 = 18 × 2
54 = 18 × 3
Both are multiples.

Q.18. Which number is a multiple of 25?

  1. 125
  2. 150
  3. 75
  4. All of these

4) All of these

📝 Description: All given numbers divide exactly by 25.

Q.19. Which number is a multiple of 2, 3, and 5?

  1. 15
  2. 30
  3. 45
  4. 60

2) 30

📝 Description:

A number divisible by 2,3,5 must be divisible by 30.
30 ÷ 30 = 1 → Correct.

Q.20. The 10th multiple of 7 is:

  1. 56
  2. 63
  3. 70
  4. 77

4) 77

📝 Description: 

10th multiple = 7 × 10 = 70 (Option C).
Correct answer is 70.

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