Interactive Practice Page on Multiples in Grade 4

Master multiples: practice exercises, examples, and applications with detailed explanations.

Practice Exercises: Finding Multiples
1 Basic Multiples
Exercise 1
List the first 5 multiples of each number:
a) 3: _______, _______, _______, _______, _______
b) 5: _______, _______, _______, _______, _______
Strategy:

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

Part a: Multiples of 3

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

First 5 multiples of 3: 3, 6, 9, 12, 15

Part b: Multiples of 5

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

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

a) 3, 6, 9, 12, 15
b) 5, 10, 15, 20, 25
Verification:

Check by dividing each multiple by the base number - should get whole numbers!

2 Identifying Multiples
Exercise 2
Circle the multiples of 6 from this list:
12, 15, 18, 24, 28, 30, 35, 36
Strategy:

Division test: Divide each number by 6 - if no remainder, it's a multiple

Step 1: Test each number

12 ÷ 6 = 2 ✓ (multiple)

15 ÷ 6 = 2.5 ✗ (not a multiple)

18 ÷ 6 = 3 ✓ (multiple)

24 ÷ 6 = 4 ✓ (multiple)

28 ÷ 6 = 4.67... ✗ (not a multiple)

30 ÷ 6 = 5 ✓ (multiple)

35 ÷ 6 = 5.83... ✗ (not a multiple)

36 ÷ 6 = 6 ✓ (multiple)

Step 2: Circle the multiples

Circled numbers: 12, 18, 24, 30, 36

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

All multiples of 6 are also multiples of both 2 and 3!

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

Listing method: List multiples of each number and find overlaps

Step 1: List multiples of 4

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...

Step 2: List multiples of 6

6, 12, 18, 24, 30, 36, 42, 48, 54, 60...

Step 3: Find common numbers

Numbers that appear in both lists: 12, 24, 36, 48...

Step 4: Select first 3

First 3 common multiples: 12, 24, 36

First 3 common multiples of 4 and 6: 12, 24, 36
Insight:

12 is the Least Common Multiple (LCM) of 4 and 6!

Practice Exercises: Advanced Problems
Multiple of n = n × k (where k = 1, 2, 3, ...)
Multiple Formula
4 Word Problem Practice
Exercise 4
A bus comes every 8 minutes and a train comes every 12 minutes. If both arrive at the station at 3:00 PM, when will they both arrive together again?
Strategy:

Find LCM: Need the Least Common Multiple of 8 and 12

Step 1: List multiples of 8

8, 16, 24, 32, 40, 48, 56, 64, 72...

Step 2: List multiples of 12

12, 24, 36, 48, 60, 72, 84...

Step 3: Find first common multiple

First common multiple: 24

Step 4: Calculate the time

They will both arrive together again in 24 minutes

3:00 PM + 24 minutes = 3:24 PM

Both will arrive together again at 3:24 PM
Problem-solving tip:

Simultaneous events require finding the LCM!

5 Pattern Recognition
Exercise 5
The first four multiples of 7 are 7, 14, 21, 28. What are the next four multiples? Describe the pattern.
Strategy:

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

28 + 7 = 35

35 + 7 = 42

42 + 7 = 49

49 + 7 = 56

Step 3: Verify with multiplication

7 × 5 = 35 ✓

7 × 6 = 42 ✓

7 × 7 = 49 ✓

7 × 8 = 56 ✓

Step 4: Describe the pattern

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

Next 4 multiples: 35, 42, 49, 56
Pattern: Add 7 to get the next multiple
Pattern insight:

All multiples of any number form an arithmetic sequence!

6 Challenge Problem
Exercise 6
Find a number that is a multiple of 2, 3, and 4. What is the smallest such number?
Strategy:

Find LCM of 2, 3, and 4: 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 4: 4, 8, 12, 16, 20, 24, 28...

Step 2: Find common multiples

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

Step 3: Identify the smallest

The smallest number divisible by 2, 3, and 4 is 12

Step 4: Verify

12 ÷ 2 = 6 ✓, 12 ÷ 3 = 4 ✓, 12 ÷ 4 = 3 ✓

The smallest number that is a multiple of 2, 3, and 4 is 12
Advanced tip:

This is called the Least Common Multiple (LCM) of 2, 3, and 4!

Multiples Practice Summary
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

Practice methods:
  1. Basic 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.
Key facts: Every number is a multiple of itself; zero is a multiple of every number; multiples form arithmetic sequences.
Practice tips: Start with basic multiplication, then move to identifying multiples, then tackle common multiples and word problems.
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 Visualization: Practice Patterns
Exercise: Multiples Comparison
Compare multiples of 3 and 5 up to 30:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 5: 5, 10, 15, 20, 25, 30
Find their common multiples and LCM.

Practice Analysis: Use the chart to identify patterns in multiples.

  • Multiples of 3: Increase by 3 each time
  • Multiples of 5: Increase by 5 each time
  • Common multiples: 15, 30
  • Least Common Multiple (LCM): 15

Questions & Answers

Question: I'm having trouble knowing when to use the LCM in word problems. How do I recognize when I need to find it?

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 bus and train example, we needed to find when both would arrive at the same time again. This means finding a time that is a multiple of both 8 and 12 minutes - 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).