LCM and HCF practice for 11+ maths
21 October 2026
LCM and HCF explained
LCM stands for Least Common Multiple. It is the smallest number that is a multiple of two or more numbers.
HCF stands for Highest Common Factor. It is the largest number that divides exactly into two or more numbers.
Both are important for 11+ maths, especially in number reasoning and word problems.
Why LCM and HCF matter
Questions on LCM and HCF appear in both CEM and GL 11+ exams. They help children spot patterns, simplify calculations, and solve real-life problems involving sharing or repeated events.
Understanding these concepts builds a strong foundation for later maths topics.
Worked example: finding LCM and HCF of 12 and 18
Step 1: List the factors of each number.
Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18
Step 2: Identify the common factors.
Common factors: 1, 2, 3, 6
Step 3: The highest common factor is the largest of these. HCF = 6.
Step 4: List the multiples of each number until a common one is found.
Multiples of 12: 12, 24, 36, 48, 60 Multiples of 18: 18, 36, 54, 72, 90
Step 5: The least common multiple is the smallest number in both lists. LCM = 36.
The correct answers are HCF = 6 and LCM = 36.
Key insight: Practising LCM and HCF helps children develop number sense, logical thinking, and the ability to break down complex problems into manageable steps. These are essential skills for success in the 11+ and beyond.
