Are HCF and LCM on the Foundation paper as well?

Yes. Spec point N4 is on both tiers, so a Foundation candidate can be asked to write a number as a product of its prime factors and to find an HCF or an LCM. The Higher versions push further: the two numbers are given as products of primes such as 2^4 3^2 7, or you are told the HCF and the LCM and asked to work back to a missing number.

How many marks are prime factors, HCF and LCM worth on Edexcel Higher?

Writing a number as a product of powers of its primes is usually 2 marks. Finding an HCF or an LCM from that factorisation is often 1 mark when the factor trees are already done, and 2-3 marks when they are not. A word problem that hides an LCM inside it runs to 3-4 marks, so budget roughly 2-5 marks per paper.

Is it true that HCF times LCM equals the two numbers multiplied together?

For two numbers, yes. The HCF of 12 and 18 is 6 and the LCM is 36, and 6 36 = 216 = 12 18. That makes it a fast check, and it also solves the reverse questions: if the HCF is 8, the LCM is 240 and one number is 40, the other is 8 240 40 = 48. The rule fails for three or more numbers, so do not use it on those.

Do I need a calculator for HCF and LCM questions?

No, and Edexcel counts on that. These questions turn up on Paper 1 as well as Papers 2 and 3, and repeated division by 2, 3, 5, 7 and 11 handles any number they are likely to set by hand. A calculator helps only with the final multiplication once you have chosen which powers to use.

HCF and LCM - Edexcel GCSE Higher Maths

Typically 2-5 marks per paper, usually a two- or three-part question in the first half · Spec 1MA1

Every whole number above 1 splits into primes in exactly one way, and the highest common factor and lowest common multiple are both built out of that split. Edexcel 1MA1 puts this at spec point N4: primes, writing a number as a product of its prime factors using index notation, and finding the HCF and LCM of two or more numbers. Both tiers are examined on it. What separates the Higher version is that the numbers are often handed to you already broken up, so the question reads $A = 2^4 \times 3^2 \times 7$ , $B = 2^3 \times 3^4 \times 5$ , find the HCF of $A$ and $B$ , and no factor tree is needed at all.

The usual shape is a two- or three-part question in the first half of a paper: write 600 as a product of powers of its prime factors, then use that answer to write down an HCF, then an LCM. It can appear on any of the three papers. Paper 1 is non-calculator, which is where repeated division by primes earns its keep, because dividing 600 by 2, by 2, by 2, by 3 and by 5 is faster by hand than hunting through factor pairs. Papers 2 and 3 tend to dress the same maths up: bells ringing together, buses leaving a station, rectangular paving slabs laid into a square. Those are LCM questions with the phrase lowest common multiple taken out.

Marks go in two predictable places. The first is answering the wrong question: the prime factors come out right, and then the HCF is written on the line where the LCM was wanted. The second belongs to the products-of-primes version, where candidates multiply $A$ and $B$ out into ordinary numbers and start from scratch, throwing away the structure the question just gave them. Write the two rules at the top of your working before you choose anything: the HCF takes the lowest power of each shared prime, the LCM takes the highest power of every prime that appears in either number. Then check with HCF $\times$ LCM $= A \times B$ , which is true for any two numbers.

Worked example

(a) Write 180 as a product of powers of its prime factors. (b) Given that

504 = 2^3 \times 3^2 \times 7

, work out the highest common factor (HCF) of 180 and 504. (c) Work out the lowest common multiple (LCM) of 180 and 504.

[5 marks]

(a) Divide 180 by primes, smallest first: $180 \div 2 = 90$ , $90 \div 2 = 45$ , $45 \div 3 = 15$ , $15 \div 3 = 5$ , and 5 is prime. The primes used are 2, 2, 3, 3, 5.
M1: a correct method carried on until every branch ends in a prime
Write them as a product in index form: $180 = 2^2 \times 3^2 \times 5$ .
A1: a product, not the list 2, 2, 3, 3, 5 and not a sum; index form is what part (a) asks for
(b) Line the two factorisations up: $180 = 2^2 \times 3^2 \times 5$ and $504 = 2^3 \times 3^2 \times 7$ . The primes in both are 2 and 3.
M1: identifying the shared primes; 5 and 7 appear in only one number each, so neither can be in the HCF
Take the lower power of each shared prime: $2^2$ from 180 and $3^2$ from either. HCF $= 4 \times 9 = 36$ .
A1: 36 as a single number, not left as $2^2 \times 3^2$ unless the question asks for a product
(c) Take the higher power of every prime that appears: $2^3 \times 3^2 \times 5 \times 7 = 8 \times 9 \times 35 = 2520$ . Check: $36 \times 2520 = 90720 = 180 \times 504$ .
A1: 2520; the check uses HCF $\times$ LCM = product of the two numbers

Practice questions

These are original questions written in Edexcel 1MA1 Higher style. Work the prime factorisation and the plain two-number HCF and LCM parts without a calculator, because that is how Paper 1 asks them. The questions that hand you $A$ and $B$ already written as products of primes are the Higher-tier variant, and they are far quicker if you never work out what $A$ and $B$ are; the bells, buses, slabs and beads questions name no method at all, which is how Edexcel writes them.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [2 marks]

Which of these is 126 written as a product of powers of its prime factors?

Answer options for question 1
$2 \times 3^2 \times 7$ $2 \times 3 \times 7$ $2^2 \times 3^2 \times 7$ $2 \times 9 \times 7$
Question 2 Exam pace [2 marks]

Which of these is 600 written as a product of powers of its prime factors?

Answer options for question 2
$2^3 \times 3 \times 5$ $2^2 \times 3 \times 5^2$ $2^3 \times 3 \times 5^2$ $2^3 \times 3^2 \times 5^2$
Question 3 Exam pace [3 marks]

At a bus station, buses to Ashford leave every 24 minutes and buses to Beckley leave every 36 minutes. A bus to each place leaves at 07:00. Work out the number of minutes after 07:00 that buses to both places next leave at the same time.

Your answer (fractions like 1/2 are fine)
Question 4 Exam pace [3 marks]

Work out the highest common factor (HCF) of 36, 60 and 84.

Your answer (fractions like 1/2 are fine)
Question 5 Exam pace [3 marks]

Work out the lowest common multiple (LCM) of 20, 30 and 40.

Your answer (fractions like 1/2 are fine)
Question 6 Stretch [3 marks]

$A = 2^a \times 3^2$ and $B = 2^3 \times 3^b$ , where $a$ and $b$ are positive integers. The highest common factor of $A$ and $B$ is 36 and the lowest common multiple is $2^3 \times 3^5$ . Work out $a$ and $b$ .

a = b =

Common mistakes examiners see

Giving the HCF when the question asked for the LCM, or the reverse. For 20 and 36 that produces 4 instead of 180.

Compare your answer with the two starting numbers before you write it on the line. An HCF is never bigger than the smaller number; an LCM is never smaller than the larger one. If 4 comes out of a question about 20 and 36 asking for a multiple, you have answered the other question.
Stopping the factor tree before every branch is prime, so 108 is written as $2^2 \times 27$ or $3 \times 36$ .

Keep splitting until every end of the tree is a prime, then circle them. 27 splits into $3 \times 3 \times 3$ and 36 into $2 \times 2 \times 3 \times 3$ , giving $108 = 2^2 \times 3^3$ . A composite number left in the answer scores the method mark at best.
Answering with a list or a sum: 2, 2, 3, 3, 3 or $2^2 + 3^3$ rather than $2^2 \times 3^3$ .

The word product means multiply, so multiplication signs have to be there. Examiner reports flag this every series: the working is right, the final line is not a product, and the accuracy mark goes. Write the multiplication signs in before you move on to part (b).
Building the LCM from the shared primes only, so the LCM of $2^3 \times 5$ and $2^2 \times 7$ comes out as $2^3 = 8$ with the 5 and the 7 dropped.

A common multiple has to be divisible by both numbers, so every prime in either number must survive. Sweep left to right through all the primes that appear anywhere, take the higher power of each, and multiply: $2^3 \times 5 \times 7 = 280$ .
Multiplying the two numbers together and calling that the LCM, giving $75 \times 90 = 6750$ instead of 450.

The product of two numbers is a common multiple but rarely the lowest, and Edexcel mark schemes name it as the answer that scores nothing. It only equals the LCM when the numbers share no prime factor. Divide the product by the HCF instead: $6750 \div 15 = 450$ .

Frequently asked questions

Are HCF and LCM on the Foundation paper as well?: Yes. Spec point N4 is on both tiers, so a Foundation candidate can be asked to write a number as a product of its prime factors and to find an HCF or an LCM. The Higher versions push further: the two numbers are given as products of primes such as $2^4 \times 3^2 \times 7$ , or you are told the HCF and the LCM and asked to work back to a missing number.
How many marks are prime factors, HCF and LCM worth on Edexcel Higher?: Writing a number as a product of powers of its primes is usually 2 marks. Finding an HCF or an LCM from that factorisation is often 1 mark when the factor trees are already done, and 2-3 marks when they are not. A word problem that hides an LCM inside it runs to 3-4 marks, so budget roughly 2-5 marks per paper.
Is it true that HCF times LCM equals the two numbers multiplied together?: For two numbers, yes. The HCF of 12 and 18 is 6 and the LCM is 36, and $6 \times 36 = 216 = 12 \times 18$ . That makes it a fast check, and it also solves the reverse questions: if the HCF is 8, the LCM is 240 and one number is 40, the other is $8 \times 240 \div 40 = 48$ . The rule fails for three or more numbers, so do not use it on those.
Do I need a calculator for HCF and LCM questions?: No, and Edexcel counts on that. These questions turn up on Paper 1 as well as Papers 2 and 3, and repeated division by 2, 3, 5, 7 and 11 handles any number they are likely to set by hand. A calculator helps only with the final multiplication once you have chosen which powers to use.

HCF and LCM - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics