Checking and securing understanding of LCM and HCF | Maths

Starter quiz

What number is written as $2^2 × 7 × 19$ as a product of its prime factors?

'532' ✓
What number is written as $2^4 × 3 × 17$ as a product of its prime factors?

'816' ✓
What number is written as $2^2 × 3^3$ as a product of its prime factors?

'108' ✓
Which of these is a prime factor of 10908?

2 ✓

5

11
Which of these is the prime factorisation of 620?

$2^2 × 5 × 23$

$2^2 × 5 × 17$

$2^2 × 5 × 31$ ✓
Which of these is the prime factorisation of 184?

$2^3 × 23$ ✓

$2^3 × 17$

$2^3 × 29$

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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.

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

Encourage students to check the reasonableness of their answer.

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.