GCSE MATHS PRACTICE

HCF and LCM Questions

HCF and LCM are both used to compare the factors and multiples of numbers.

The highest common factor (HCF) is the largest factor shared by two or more numbers. The lowest common multiple (LCM) is the smallest positive multiple shared by two or more numbers.

Try the example and four practice questions below, then continue in Maths Unlocked for the full lesson and more practice.

Updated 30 September 2026

Highest common factor (HCF)

The largest number that divides exactly into each of the given numbers.

Lowest common multiple (LCM)

The smallest positive number that is a multiple of each of the given numbers.

Worked example

Find the HCF and LCM of 24 and 36.

Use prime factorisation: 24 = 2 × 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3.
For the HCF, use the prime factors shared by both numbers: 2 × 2 × 3 = 12. So the HCF is 12.
For the LCM, use every prime factor needed to make both numbers: 2 × 2 × 2 × 3 × 3 = 72. So the LCM is 72.

Answer: HCF = 12; LCM = 72

Practice questions

1
Find the HCF of 18 and 30.
2
Find the LCM of 8 and 12.
3
Find the HCF of 36 and 54.
4
Two lights flash at regular intervals. One flashes every 6 seconds and the other every 8 seconds. They flash together now. After how many seconds will they next flash together?

Show answers

1. 6
2. 24
3. 18
4. 24 seconds

Common mistakes

Mixing up HCF and LCM — HCF is about shared factors. LCM is about shared multiples.
Choosing a common factor that is not the highest — Two numbers can have several common factors. The HCF must be the largest one.
Stopping at the first multiple of one number — For LCM, the number must be a multiple of both numbers.

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HCF and LCM Questions

HCF and LCM are both used to compare the factors and multiples of numbers.

The highest common factor (HCF) is the largest factor shared by two or more numbers. The lowest common multiple (LCM) is the smallest positive multiple shared by two or more numbers.

Try the example and four practice questions below, then continue in Maths Unlocked for the full lesson and more practice.

Updated 30 September 2026

Worked example

Find the HCF and LCM of 24 and 36.

Use prime factorisation: 24 = 2 × 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3.

For the HCF, use the prime factors shared by both numbers: 2 × 2 × 3 = 12. So the HCF is 12.

For the LCM, use every prime factor needed to make both numbers: 2 × 2 × 2 × 3 × 3 = 72. So the LCM is 72.

Answer: HCF = 12; LCM = 72

Common mistakes

Mixing up HCF and LCM — HCF is about shared factors. LCM is about shared multiples.

Choosing a common factor that is not the highest — Two numbers can have several common factors. The HCF must be the largest one.

Stopping at the first multiple of one number — For LCM, the number must be a multiple of both numbers.

HCF and LCM Questions

Highest common factor (HCF)

Lowest common multiple (LCM)

Worked example

Practice questions

Common mistakes

Related resources

More Maths Unlocked lessons

HCF and LCM Questions

Highest common factor (HCF)

Lowest common multiple (LCM)

Worked example

Practice questions

Common mistakes

Related resources

More Maths Unlocked lessons