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HCF and Lowest Common Multiple (F)

Find HCF and LCM on GCSE Foundation. Use prime factors, factor trees, and multiples to solve timetable, packaging, and fraction problems quickly.

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Fascinating Fact:

For bus timetables, buses every 15 and 20 minutes meet again after LCM(15, 20) = 60 minutes. Listing multiples finds the first common one quickly.

In GCSE Maths (Foundation), HCF and LCM are found using prime factorisation, factor trees, or Venn diagrams. You’ll apply them to schedules, product packs, and simplifying or adding fractions.

Key Terms

Highest Common Factor (HCF): The biggest number that divides two or more numbers exactly.
Lowest Common Multiple (LCM): The smallest number that is a multiple of two or more numbers.
Prime factorisation: Writing a number as a product of prime numbers (e.g., 60 = 2² × 3 × 5).

Frequently Asked Questions (Click to see answers)

How do I find the HCF of two numbers?

Prime factorise both numbers, then multiply the primes they share with the lowest powers. Example: 36 = 2²×3², 48 = 2&sup4;×3. HCF = 2²×3 = 12.

What is the quickest way to find the LCM?

Use prime factors with highest powers or list multiples until the first match. For 12 and 18: 12 = 2²×3, 18 = 2×3²; LCM = 2²×3² = 36.

When do I use HCF and when do I use LCM in word problems?

Use HCF to share or group items equally without leftovers. Use LCM to find when events coincide or to match sizes for common repeats, like timetables.