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Year 10
Higher

Checking and securing understanding of LCM and HCF

I can calculate the lowest common multiple or highest common factor efficiently.

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New
New
Year 10
Higher

Checking and securing understanding of LCM and HCF

I can calculate the lowest common multiple or highest common factor efficiently.

Download all resources
arrow-right
Share activities with pupils
arrow-right
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Lesson details

Key learning points

  1. Both the LCM and HCF can be found by comparing the prime factorisation of the numbers.
  2. A Venn diagram can be a helpful representation.
  3. This representation can be extended to consider three numbers.
  4. The context of the question can make it clear whether the LCM or HCF would be the most useful.

Keywords

  • HCF - HCF is an abbreviation for highest common factor.

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

  • Prime factorisation - Prime factorisation is a method to find the prime factors of a given integer.

  • Product of primes - Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

Common misconception

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

Encourage students to check the reasonableness of their answer.

Give pupils Venn diagrams with the prime factors filled in and ask them what numbers are represented and what the HCF and LCM are. Often pupils forget that the integer can be found by finding the product of one set in the Venn diagram.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
What number is written as $$2^2 × 7 × 19$$ as a product of its prime factors?
Correct Answer: 532
Q2.
What number is written as $$2^4 × 3 × 17$$ as a product of its prime factors?
Correct Answer: 816
Q3.
What number is written as $$2^2 × 3^3 $$ as a product of its prime factors?
Correct Answer: 108
Q4.
Which of these is a prime factor of 10908?
Correct answer: 2
5
11
Q5.
Which of these is the prime factorisation of 620?
$$2^2 × 5 × 23$$
$$2^2 × 5 × 17$$
Correct answer: $$2^2 × 5 × 31$$
Q6.
Which of these is the prime factorisation of 184?
Correct answer: $$2^3 × 23$$
$$2^3 × 17$$
$$2^3 × 29$$

Exit quiz

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6 Questions

Q1.
What is the lowest common multiple of 32 and 48?
Correct Answer: 96
Q2.
What is the lowest common multiple of 32 and 50?
Correct Answer: 800
Q3.
What is the lowest common multiple of 30 and 48?
Correct Answer: 240
Q4.
What is the highest common factor of 32 and 48?
Correct Answer: 16
Q5.
What is the highest common factor of 32 and 50?
Correct Answer: 2
Q6.
What is the highest common factor of 32, 12 and 48?
Correct Answer: 4