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Year 10 - Maths

Checking and securing understanding of LCM and HCF

Arithmetic procedures: index laws

In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.

You will learn to calculate the lowest common multiple or highest common factor efficiently.

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

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.

1. Solve this in steps: explain the method from this lesson and why each step matters.

Both the LCM and HCF can be found by comparing the prime factorisation of the numbers. A Venn diagram can be a helpful representation.

2. Use this key word in a maths sentence and explain it clearly. 'HCF'

HCF is an abbreviation for highest common factor. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: When using a Venn diagram students often mix up HCF & LCM. Correction: Encourage students to check the reasonableness of their answer.