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Year 7

HCF or LCM

I can use the prime factorisation of two or more positive integers to efficiently find either the highest common factor or lowest common multiple, depending on the context of the question.

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New
New
Year 7

HCF or LCM

I can use the prime factorisation of two or more positive integers to efficiently find either the highest common factor or lowest common multiple, depending on the context of the question.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. It may be necessary to find the HCF in real world situations
  2. It may be necessary to find the LCM in real world situations
  3. It is important to identify which of the LCM and HCF are needed in real world situations
  4. The LCM and HCF can be found in a variety of different contexts

Common misconception

When using a Venn diagram students often mix up HCF & LCM.

Encourage students to check the reasonableness of their answer.

Keywords

  • HCF - HCF is an abbreviation for highest common factor

  • LCM - LCM is an abbreviation for lowest common factor

To introduce the idea of HCF give students 2 sets of counters which they need to sort into groups of the same size. Start with pairs which only have 1 common factor and move onto pairs with 2, etc. The numbers chosen can be tailored to the students.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
What does the M stand for in LCM?
Correct Answer: multiple
Q2.
Which of the following is not a multiple of $$2^2\times3\times5$$?
$$2^3\times3^2\times5^3$$
Correct answer: $$2\times3^2\times5^3$$
$$2^4\times3\times5^3$$
$$2^5\times3^2\times5^3\times7$$
Q3.
Given $$12 = 2^2\times3$$, write 84 as a product of its prime factors.
$$2^2\times3\times5$$
Correct answer: $$2^2\times3\times7$$
$$2^2\times3^2\times7$$
$$2^2\times3^2$$
Q4.
The LCM of 54 and 90 is
An image in a quiz
Correct Answer: 270, two hundred and seventy
Q5.
The LCM of 70 and 42 is 210. The missing prime factor in the Venn diagram is
An image in a quiz
Correct Answer: 2, two
Q6.
The LCM of 6, 10 and 42 is
An image in a quiz
Correct Answer: 210, two hundred and ten

Exit quiz

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6 Questions

Q1.
What does HCF stand for?
Correct Answer: highest common factor, Highest Common Factor
Q2.
Sofia goes to her gran's every 6th day and goes to the park every 8th day. Sofia wants to know on what day she does both. Does she need to find the HCF or the LCM?
Correct Answer: LCM, lowest common multiple
Q3.
Sofia goes to her gran's every 6th day and goes to the park every 8th day. Complete the statement: On the th day Sofia does both.
Correct Answer: 24, 24th, twenty-four
Q4.
Alex has 12 white flowers, 45 red flowers and 30 yellow flowers. He wants to make identical bunches. What is the greatest number of bunches he can make?
2
Correct answer: 3
4
5
Q5.
Laura goes to a club every 4 days, Andeep goes every 12 days and Lucas goes every 10 days. They all went today. How can you work out how many days it will be until they all go on the same day again?
Correct answer: Find the LCM.
Find the HCF
Q6.
Laura goes to a club every 4 days, Andeep goes to the club every 12 days and Lucas goes every 10 days. They all went today. How many days will it be until they all go on the same day again?
Correct Answer: 60, sixty, 60 days, sixty days