WorksheetsAbout this worksheet
The HCF (highest common factor) of two numbers is the biggest number that divides both. The LCM (lowest common multiple) is the smallest number that both divide. For 12 and 18 the HCF is 6 and the LCM is 36.
What this skill is
A factor of a number divides it exactly; a multiple of a number is in its table. Two numbers usually share some factors, and the biggest shared one is the HCF. Their tables meet again and again, and the first meeting place is the LCM. The HCF is used to simplify fractions; the LCM is used to add fractions with different denominators.
A worked example
Find the HCF and LCM of 24 and 36 by prime factors.
- 24 = 2 × 2 × 2 × 3
- 36 = 2 × 2 × 3 × 3
- HCF: take what both lists share. Two 2s and one 3: 2 × 2 × 3 = 12.
- LCM: take each prime the greatest number of times it appears in either list. Three 2s and two 3s: 2 × 2 × 2 × 3 × 3 = 72.
Check: HCF × LCM = 12 × 72 = 864, and 24 × 36 = 864.
Tips for parents and teachers
- Use prime factorisation or the division method, whichever the school teaches, and keep to one until it is sure.
- A useful check: HCF times LCM equals the product of the two numbers. 6 times 36 = 216 = 12 times 18.
- The HCF can never be bigger than the smaller number; the LCM can never be smaller than the bigger number.
How to use this sheet at home and in class
- At home: for small numbers, let the child list the factors of both and circle the common ones. Listing shows what the words mean before any method is used.
- In class: "Smaller numbers" for the first lessons, where listing still works; "Bigger numbers" once a method has been taught.
- Give word problems beside the sheet. "Largest tile that fits both sides" is HCF; "bells ringing together again" is LCM.
Mistakes to watch for
- Mixing up the two names. The HCF is the smaller answer, at most the smaller number; the LCM is the bigger answer, at least the bigger number.
- Taking the product of the two numbers as the LCM. It is a common multiple, but usually not the lowest: for 24 and 36 the product is 864 and the LCM is 72.
- Stopping the factorisation too early, at a number such as 4 or 9 that is not prime.
What to try next
- Fractions worksheets: where HCF and LCM are put to work.
- Times tables worksheets: if factors are slow to come.
- Division worksheets: the division method needs it.