HCF & LCM
This topic covers 4 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Factors & Multiples Review
Recap factors and multiples before HCF/LCM - Highest Common Factor
Find the HCF of two or more numbers - Lowest Common Multiple
Find the LCM of two or more numbers - Challenge — HCF & LCM Word Problems
Apply HCF and LCM to solve real-world problems
Before This Topic
Your child should be comfortable with:
- Prime & Composite Numbers (Year 5)
- Multiplication Tables (Year 4)
Common Mistakes
- Mixing up HCF and LCM (giving the largest shared factor when asked for the smallest shared multiple, or vice versa)
HCF = Highest Common Factor — the biggest number that divides evenly into both. LCM = Lowest Common Multiple — the smallest number that both divide into. HCF of 12 and 18 is 6; LCM of 12 and 18 is 36. - Listing only some factors or multiples and missing the answer (e.g. forgetting that 1 and the number itself are always factors)
Work systematically: list factor pairs starting from 1 upwards. For 12: 1×12, 2×6, 3×4 — so the factors are 1, 2, 3, 4, 6, 12. For multiples, write out the times table for each number until you spot a match.
Tips for Parents
- Use Venn diagrams with prime factors: break each number into primes, put shared primes in the overlap. HCF = multiply the overlap; LCM = multiply everything in the diagram.
- Make it real: "You buy hot dog rolls in packs of 6 and sausages in packs of 8. What is the smallest number you need so you have no leftovers?" That is the LCM (24).
- Practise prime factor trees — draw them like actual trees with branches splitting until every leaf is a prime number. Children often enjoy the drawing aspect.
- Connect HCF to simplifying fractions: "The HCF of 12 and 18 is 6, so 12/18 simplifies to 2/3 by dividing both by 6." This shows why HCF is useful.
Key Words
- Factor — A number that divides evenly into another — 4 is a factor of 12 because 12 ÷ 4 = 3 with no remainder.
- Multiple — A number in a times table — 12, 18, 24, 30 are all multiples of 6.
- HCF (Highest Common Factor) — The largest number that divides evenly into two or more numbers — the HCF of 12 and 18 is 6.
- LCM (Lowest Common Multiple) — The smallest number that two or more numbers all divide into — the LCM of 4 and 6 is 12.
- Prime factor — A factor that is also a prime number — the prime factors of 12 are 2 and 3 (since 12 = 2 × 2 × 3).
Where This Fits
Before this topic: Children should know their times tables fluently, understand factors and multiples, and be able to identify prime numbers.
After this topic: HCF and LCM are essential for simplifying fractions, adding fractions with unlike denominators, and working with algebraic fractions in later years.
How MathCraft Teaches This
In MathCraft, HCF & LCM is taught through the Algebra & Arithmetic adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 4 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise HCF & LCM with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
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