Basic 4 · Mathematics · Counting, Representation and Cardinality
Multiples and the Lowest Common Multiple (LCM)
In this topic you will list multiples and find the lowest common multiple of two numbers up to 100.
By the end of these notes you should be able to:
- List multiples of a number
- Find common multiples of two numbers
- Find the lowest common multiple
What you already know
- Factors
Copy everything that has a blue line on its left into your notebook. The other parts are for reading.
- Strand
- Number
- Sub-strand
- Counting, Representation and Cardinality
- Indicator
- B4.1.1.3.3 – Determine the lowest common multiple (LCM) of at least two given numbers up to 100
Introduction
Kofi visits the library every 4 days. Ama visits every 6 days. If they both visit today, when will they next meet at the library? We use multiples to find out.
1. Multiples
Multiple: The answer when a number is multiplied by a whole number.
| Number | First multiples |
|---|---|
| 4 | 4, 8, 12, 16, 20, 24, 28 |
| 6 | 6, 12, 18, 24, 30, 36 |
2. Common Multiples and LCM
Common multiple: A number that is a multiple of two or more numbers.
Lowest common multiple (LCM): The smallest common multiple.
Example
Find the LCM of 4 and 6.
- Multiples of 4: 4, 8, 12, 16, 20, 24 …
- Multiples of 6: 6, 12, 18, 24 …
- Common multiples: 12, 24 …
Answer: LCM of 4 and 6 = 12. Kofi and Ama meet again in 12 days.
| Numbers | LCM |
|---|---|
| 2 and 3 | 6 |
| 3 and 5 | 15 |
| 6 and 8 | 24 |
| 4 and 10 | 20 |
| 2, 3 and 4 | 12 |
Tip: Multiples of the bigger number first: list multiples of 8 (8, 16, 24) and stop at the first one 6 divides.
New words
- multiple
- A number in a number's times table.
- common
- Shared by two or more.
- lowest
- Smallest.
- LCM
- Lowest common multiple.
- list
- To write one after another.
- times table
- The multiples of a number in order.
Summary
- Multiples are the numbers in a times table.
- Common multiples are shared by two or more numbers.
- The LCM is the smallest common multiple.
- LCM of 4 and 6 is 12.
Class activity: Clap and Stamp
- Count from 1 to 30 together.
- Clap on multiples of 3 and stamp on multiples of 5.
- The first number where you clap and stamp is the LCM (15).
You need: Bottle tops, Locally made number cards, Exercise books
Exercises
Answer in your exercise book first, then check your answers.
1. Which is a multiple of 7?
- A. 21
- B. 17
- C. 27
- D. 15
Show answer
Answer: 217 × 3 = 21.2. What is the LCM of 3 and 4?
- A. 12
- B. 7
- C. 24
- D. 1
Show answer
Answer: 1212 is the first common multiple.3. What is the LCM of 5 and 10?
- A. 10
- B. 50
- C. 5
- D. 15
Show answer
Answer: 1010 is a multiple of both.4. 24 is a common multiple of 6 and 8.
- A. True
- B. False
Show answer
Answer: True6 × 4 and 8 × 3.5. The LCM of 6 and 9 is 54.
- A. True
- B. False
Show answer
Answer: FalseIt is 18.6. The first five multiples of 9 are 9, 18, 27, 36 and ______.
Show answer
Answer: 459 × 5 = 45.7. Find the LCM of 8 and 12.
Show answer
Answer: 24Multiples of 12: 12, 24; 24 ÷ 8 = 3.8. One bell rings every 6 minutes and another every 10 minutes. They ring together at 8:00. When will they next ring together?
Show answer
Answer: 8:30LCM of 6 and 10 is 30 minutes.
Homework
- Find the LCM of 2, 5 and 10. Show your lists of multiples.