Comprehensive Multiples Practice PDF for Grade 4

Complete multiples practice worksheet with exercises, examples, and detailed solutions.

Practice Exercises: Basic Multiples
1 Finding Multiples
Exercise 1A
List the first 6 multiples of each number:
a) 2: _______, _______, _______, _______, _______, _______
b) 3: _______, _______, _______, _______, _______, _______
c) 5: _______, _______, _______, _______, _______, _______
Method:

Multiplication method: Multiply the base number by 1, 2, 3, 4, 5, 6

Part a: Multiples of 2

2 × 1 = 2, 2 × 2 = 4, 2 × 3 = 6, 2 × 4 = 8, 2 × 5 = 10, 2 × 6 = 12

First 6 multiples of 2: 2, 4, 6, 8, 10, 12

Part b: Multiples of 3

3 × 1 = 3, 3 × 2 = 6, 3 × 3 = 9, 3 × 4 = 12, 3 × 5 = 15, 3 × 6 = 18

First 6 multiples of 3: 3, 6, 9, 12, 15, 18

Part c: Multiples of 5

5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15, 5 × 4 = 20, 5 × 5 = 25, 5 × 6 = 30

First 6 multiples of 5: 5, 10, 15, 20, 25, 30

a) 2, 4, 6, 8, 10, 12
b) 3, 6, 9, 12, 15, 18
c) 5, 10, 15, 20, 25, 30
Verification:

Check: Each multiple divided by the base number equals a whole number!

2 Identifying Multiples
Exercise 2A
Circle the multiples of 4 from this list:
8, 12, 15, 16, 20, 22, 24, 28, 30, 32
Method:

Division test: Divide each number by 4 - if no remainder, it's a multiple

Step 1: Test each number

8 ÷ 4 = 2 ✓ (multiple)

12 ÷ 4 = 3 ✓ (multiple)

15 ÷ 4 = 3.75 ✗ (not a multiple)

16 ÷ 4 = 4 ✓ (multiple)

20 ÷ 4 = 5 ✓ (multiple)

22 ÷ 4 = 5.5 ✗ (not a multiple)

24 ÷ 4 = 6 ✓ (multiple)

28 ÷ 4 = 7 ✓ (multiple)

30 ÷ 4 = 7.5 ✗ (not a multiple)

32 ÷ 4 = 8 ✓ (multiple)

Step 2: Circle the multiples

Circled numbers: 8, 12, 16, 20, 24, 28, 32

Multiples of 4: 8, 12, 16, 20, 24, 28, 32
Pattern:

All multiples of 4 are also multiples of 2, and they're always even!

3 Common Multiples
Exercise 3A
Find the first 4 common multiples of 3 and 6.
Method:

Listing method: List multiples of each number and find overlaps

Step 1: List multiples of 3

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...

Step 2: List multiples of 6

6, 12, 18, 24, 30, 36, 42, 48...

Step 3: Find common numbers

Numbers that appear in both lists: 6, 12, 18, 24, 30, 36...

Step 4: Select first 4

First 4 common multiples: 6, 12, 18, 24

First 4 common multiples of 3 and 6: 6, 12, 18, 24
Observation:

Since 6 is a multiple of 3, all multiples of 6 are also multiples of 3!

Advanced Practice: Word Problems
Multiple of n = n × k (where k = 1, 2, 3, ...)
Multiple Formula
4 Word Problem Practice
Exercise 4A
A bakery delivers bread every 4 days and pastries every 6 days. If both deliveries happen today, in how many days will both deliveries happen on the same day again?
Method:

Find LCM: Need the Least Common Multiple of 4 and 6

Step 1: List multiples of 4

4, 8, 12, 16, 20, 24, 28, 32, 36...

Step 2: List multiples of 6

6, 12, 18, 24, 30, 36, 42...

Step 3: Find first common multiple

First common multiple: 12

Step 4: Answer the question

Both deliveries will happen on the same day again in 12 days

Both deliveries will happen together again in 12 days
Problem-solving tip:

When events repeat at different intervals, find the LCM to see when they coincide!

5 Pattern Recognition
Exercise 5A
The first five multiples of 7 are 7, 14, 21, 28, 35. What are the next five multiples? Describe the pattern.
Method:

Arithmetic sequence: Add 7 to get the next multiple

Step 1: Identify the pattern

Each multiple is 7 more than the previous one

Step 2: Continue the sequence

35 + 7 = 42

42 + 7 = 49

49 + 7 = 56

56 + 7 = 63

63 + 7 = 70

Step 3: Verify with multiplication

7 × 6 = 42 ✓, 7 × 7 = 49 ✓, 7 × 8 = 56 ✓, 7 × 9 = 63 ✓, 7 × 10 = 70 ✓

Step 4: Describe the pattern

Multiples of 7 form an arithmetic sequence with a common difference of 7

Next 5 multiples: 42, 49, 56, 63, 70
Pattern: Add 7 to get the next multiple
Pattern insight:

All multiples of any number form an arithmetic sequence with the number as the common difference!

6 Challenge Problem
Exercise 6A
Find a number that is a multiple of 2, 3, and 6. What is the smallest such number?
Method:

Find LCM of 2, 3, and 6: Need the smallest number divisible by all three

Step 1: List multiples of each

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...

Multiples of 6: 6, 12, 18, 24, 30, 36...

Step 2: Find common multiples

Numbers that appear in all three lists: 6, 12, 18, 24...

Step 3: Identify the smallest

The smallest number divisible by 2, 3, and 6 is 6

Step 4: Verify

6 ÷ 2 = 3 ✓, 6 ÷ 3 = 2 ✓, 6 ÷ 6 = 1 ✓

The smallest number that is a multiple of 2, 3, and 6 is 6
Advanced insight:

Since 6 is a multiple of both 2 and 3, the LCM of 2, 3, and 6 is 6!

Comprehensive Review: Multiples Concepts
Multiple of n = n × k (where k = 1, 2, 3, ...)
Core Formula
Key definitions:

Multiple: A number that results from multiplying another number by a whole number

Common Multiple: A number that is a multiple of two or more numbers

Least Common Multiple (LCM): The smallest positive number that is a multiple of two or more numbers

Problem-solving methods:
  1. Finding multiples: Multiply by 1, 2, 3, 4, 5...
  2. Identifying multiples: Divide and check for whole number results
  3. Common multiples: List multiples of each and find overlaps
  4. Word problems: Look for LCM when events happen simultaneously
  5. Verification: Always check answers by reversing operations
Tip 1: Use multiplication tables to quickly identify multiples.
Tip 2: Multiples of 2 are even numbers (end in 0, 2, 4, 6, 8).
Tip 3: Multiples of 5 end in 0 or 5.
Tip 4: For large numbers and 4, check if last two digits form a multiple of 4.
Tip 5: The smallest positive multiple of any number is the number itself.
Tip 6: When one number is a multiple of another, the LCM is the larger number.
Key facts: Every number is a multiple of itself; zero is a multiple of every number; multiples form arithmetic sequences.
Common mistakes: Confusing multiples with factors; forgetting that 0 is a multiple of every number; thinking multiples stop after a few numbers.
Essential formulas and rules:

• Multiple of n = n × k (where k is any positive integer)

• To check if A is a multiple of B: A ÷ B should result in a whole number

• Common multiples of A and B are numbers divisible by both A and B

• The Least Common Multiple (LCM) is the smallest positive common multiple

• Multiples of any number form an infinite arithmetic sequence

Multiples Practice: Visualization and Patterns
Exercise: Comparing Multiples
Compare multiples of 2, 3, and 4 up to 24:
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24
Multiples of 4: 4, 8, 12, 16, 20, 24
Find their common multiples and LCM.

Analysis: Use the chart to identify patterns in multiples.

  • Multiples of 2: Increase by 2 each time (even numbers)
  • Multiples of 3: Increase by 3 each time
  • Multiples of 4: Increase by 4 each time (also multiples of 2)
  • Common multiples of 2, 3, and 4: 12, 24
  • Least Common Multiple (LCM) of 2, 3, and 4: 12

Questions & Answers

Question: I'm struggling with word problems involving multiples. How do I know when to use LCM?

Answer: Great question! Look for these key phrases in word problems that suggest you need the LCM:

  • "When will they meet again?" or "when will they both happen?"
  • "How often do they coincide?" or "at what interval do they match?"
  • "What is the next time both events happen together?"
  • "Finding the earliest time when multiple things happen simultaneously"

In our bakery example, we needed to find when both deliveries would happen on the same day again. This means finding a time that is a multiple of both 4 and 6 days - that's exactly what LCM does!

The LCM gives you the smallest number that both (or all) numbers divide into evenly.

Question: Is there a faster way to find common multiples without listing all of them?

Answer: Yes, there are some strategies that can help:

  • For small numbers: List multiples of the larger number and see which ones the smaller number also divides evenly
  • Look for patterns: If one number is a multiple of the other, the LCM is the larger number
  • Use prime factorization: Break numbers into prime factors and take the highest power of each

Example: For 6 and 9

  • Multiples of 9: 9, 18, 27, 36...
  • Does 6 divide these? 9÷6=1.5 (no), 18÷6=3 (yes!) → LCM is 18

For now, listing multiples is the most reliable method for grade 4 students. As you advance, you'll learn more sophisticated methods!

Question: I sometimes confuse multiples with factors. How can I remember the difference?

Answer: This is a common confusion! Here's a memory aid:

  • Factors: Numbers that DIVIDE INTO another number (go inside the number)
  • Multiples: Numbers that RESULT FROM multiplying a number (come after the number)

Think of it this way:

  • Factors of 12: 1, 2, 3, 4, 6, 12 (these divide into 12)
  • Multiples of 12: 12, 24, 36, 48... (these come after 12 when multiplying)

Memory trick: "F" comes before "M" in the alphabet, just like factors are smaller numbers that fit into a number, while multiples are larger numbers that come after.

Also, remember: factors make numbers smaller (through division), multiples make numbers larger (through multiplication).