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Lesson 17 of 19
  • Year 7

Lowest common multiple

I can use the prime factorisation of two or more positive integers to efficiently find their lowest common multiple.

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View unit
Lesson 17 of 19
New
New
  • Year 7

Lowest common multiple

I can use the prime factorisation of two or more positive integers to efficiently find their lowest common multiple.

Download all resources
Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. Common multiples can be found using the prime factorisation of numbers
  2. The lowest common multiple of two numbers can be found by comparing the prime factorisation of both numbers
  3. Sometimes a Venn diagram can help identify the lowest common multiple of two numbers
  4. The lowest common multiple of more than two numbers can be found using prime factorisation

Keywords

  • Lowest common multiple - The lowest common multiple is the lowest number that is a multiple of two or more integers.

  • LCM - LCM is an abbreviation for lowest common multiple.

Common misconception

When using a Venn diagram misplacement of factors is common.

Encourage students to check that the product of factors in each set is the correct integer.


To help you plan your year 7 maths lesson on: Lowest common multiple, download all teaching resources for free and adapt to suit your pupils' needs...

Before going through writing multiples of integers given in prime factor form get the students to try doing this themselves on mini whiteboards. Most students will probably evaluate the product, which will lead into using the prime factor form.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Complete the statement. A number that is a multiple of two or more numbers is called a multiple.

Correct Answer: common

Q2.
Match each number with its first four multiples.

Correct Answer:First four multiples of 2:,2, 4, 6, 8

2, 4, 6, 8

Correct Answer:First four multiples of 4:,4, 8, 12, 16

4, 8, 12, 16

Correct Answer:First four multiples of 3:,3, 6, 9, 12

3, 6, 9, 12

Correct Answer:First four multiples of 12:,12, 24, 36, 48

12, 24, 36, 48

Q3.
Which of the following is a factor of $$2^3\times3^4\times5^2$$ and of $$2^3\times3^5\times5$$?

$$2^3\times3^5\times5^2$$
Correct answer: $$2^2\times3^4\times5$$
$$2^3\times3^4\times5^2$$

Q4.
Select the correct statements.

An image in a quiz
Correct answer: 240 as a product of prime factors is $$2^4 \times 3 \times 5$$
240 as a product of prime factors is $$2^2 \times 3^2 \times 5$$
180 as a product of prime factors is $$2^2 \times 3 \times 5$$
Correct answer: 180 as a product of prime factors is $$2^2 \times 3^2 \times 5$$

Q5.
The HCF of 84, 180 and 120 is .

An image in a quiz
Correct Answer: 12, twelve

Q6.
The HCF of 126, 945 and 189 is 63. The missing prime factor in the Venn diagram is .

An image in a quiz
Correct Answer: 7, seven

Assessment exit quiz

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6 Questions

Q1.
What does the L stand for in LCM?

Correct Answer: lowest, least

Q2.
Which of the following is not a multiple of $$2\times3^2\times5$$?

$$2^2\times3^2\times5$$
$$2^2\times3^3\times5$$
Correct answer: $$2^2\times3\times5$$
$$2^2\times3^2\times5^3$$

Q3.
Given that $$12 = 2^2\times3$$, write 60 as a product of its prime factors.

$$2^3\times3$$
$$2^2\times3\times12$$
$$2^2\times3^2\times5$$
Correct answer: $$2^2\times3\times5$$

Q4.
The LCM of 18 and 30 is

An image in a quiz
Correct Answer: 90, ninety

Q5.
The LCM of 70 and 42 is 210. So, the missing prime factor in the Venn diagram is

An image in a quiz
Correct Answer: 7, seven

Q6.
The LCM of 12, 20 and 84 is

An image in a quiz
Correct Answer: 420, four hundred and twenty