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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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Lesson 18 of 19

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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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Lesson details

Key learning points

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

Keywords

HCF - HCF is an abbreviation for highest common factor.
LCM - LCM is an abbreviation for lowest common factor.

Common misconception

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

Encourage students to check the reasonableness of their answer.

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.

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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).

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Worksheet

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Prior knowledge 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

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

Correct Answer: 2, two

Q6.
The LCM of 6, 10 and 42 is

Correct Answer: 210, two hundred and ten

Assessment 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?

Correct answer: 3

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

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UnitMaths / Properties of number: factors, multiples, squares and cubes

Maths

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HCF or LCM

HCF or LCM

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Equipment

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.What does the M stand for in LCM?

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

Q3.Given $$12 = 2^2\times3$$, write 84 as a product of its prime factors.

Q4.The LCM of 54 and 90 is

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

Q6.The LCM of 6, 10 and 42 is

Assessment exit quiz

6 Questions

Q1.What does HCF stand for?

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?

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.

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?

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?

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?

Lesson appears in

UnitMaths / Properties of number: factors, multiples, squares and cubes

Maths

Q1.
What does the M stand for in LCM?

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

Q3.
Given $$12 = 2^2\times3$$, write 84 as a product of its prime factors.

Q4.
The LCM of 54 and 90 is

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

Q6.
The LCM of 6, 10 and 42 is

Q1.
What does HCF stand for?

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?

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.

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?

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?

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?