A worksheet on finding the HCF and the LCM of two numbers written as a product of their prime factors, using prime factorization. Detailed solutions are provided.

Master number theory with this comprehensive Highest Common Factor (HCF) and Lowest Common Multiple (LCM) worksheet! Designed perfectly for Key Stage 3 maths students (Year 7 and Year 8), this resource focuses on finding common factors and multiples directly from numbers written as products of prime factors using indices.

Are you looking for a rigorous, no-prep resource to help your secondary students master prime factors without drawing basic factor trees over and over? This structured practice worksheet is perfectly designed to help students determine the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) using expanded prime products and exponential index notation.
By bypassing introductory tree drawing, these drills challenge students to apply index laws to isolate the correct overlapping bases for the HCF and accumulate the maximum prime factors for the LCM. With completely clean, maths-focused layouts and zero visual distraction, this resource is excellent for independent desk work, homework assignments, or emergency cover lessons.

What’s Included in This Worksheet?
• Core Prime Factor Product Drills: Practice questions featuring integer values A and B pre-factored into prime bases raised to various whole-number powers.
• Rigorous Calculations: Questions progress from double-digit responses to multi-digit number evaluations (reaching values over 100,000) to build true mathematical fluency.
• Full Solutions Provided: Includes a complete step-by-step printed answer key that explicitly shows the prime product setups and the final multi-digit arithmetic calculations for quick grading or student self-marking.

Perfect For:
• Independent Classwork or Main Lesson Tasks
• Differentiated Homework Assignments
• KS3 Maths Revision & GCSE Foundation Preparation
• Fast Finishers or Targeted Intervention Groups
• Quick, No-Prep Emergency Cover Work

Curriculum Alignment:
• UK National Curriculum: Fits perfectly into the Key Stage 3 (KS3) Number framework, focusing on using the concepts and vocabulary of prime numbers, highest common factor, lowest common multiple, and prime factorisation (including using index notation).