Given HCF & LCM - Find Possible Numbers WORKSHEET
Suitable for Year groups: Year 8, Year 9
GCSE Tier: Foundation/Higher
Targeting grades: 4-5
Prerequisite knowledge: Calculating HCF and LCM for whole numbers. Prime factorisation and use of Venn diagrams for HCF/LCM. Basic manipulation of algebraic expressions with common factors.
Given HCF & LCM - Find Possible Numbers WORKSHEET DESCRIPTION
Challenge students with a series of ‘reverse’ highest common factor (HCF) and lowest common multiple (LCM) problems.
Learners begin by using Venn diagrams to find the HCF and LCM of given number pairs, then progress to finding a missing number when the HCF, LCM, and one value are provided. Section B introduces open-ended tasks where pupils create their own pairs of numbers to meet specified HCF and LCM conditions. Section C extends the challenge to algebraic expressions, applying the same reasoning about factors and multiples with variables as well as numbers.
This steady progression from straightforward numerical cases to algebraic reasoning develops both fluency and problem-solving skills while deepening understanding of the relationships between factors, multiples, and products.
Learners begin by using Venn diagrams to find the HCF and LCM of given number pairs, then progress to finding a missing number when the HCF, LCM, and one value are provided. Section B introduces open-ended tasks where pupils create their own pairs of numbers to meet specified HCF and LCM conditions. Section C extends the challenge to algebraic expressions, applying the same reasoning about factors and multiples with variables as well as numbers.
This steady progression from straightforward numerical cases to algebraic reasoning develops both fluency and problem-solving skills while deepening understanding of the relationships between factors, multiples, and products.
