LCM and HCF practice for 11+ Maths
21 October 2026
Why LCM and HCF matter in 11+ Maths
Understanding LCM (Lowest Common Multiple) and HCF (Highest Common Factor) is essential for 11+ Maths. These concepts appear in many exam questions, especially when working with fractions, ratios or solving problems about sharing and grouping. Practising these skills helps children spot patterns and solve questions quickly.
Key insight:
LCM is used when you need to find the first time two events happen together, such as two lights flashing at different intervals. HCF is useful when dividing things into the largest possible equal groups, like splitting a set of objects fairly.
Worked example
Find the LCM and HCF of 12 and 18.
Step 1: Write each number as a product of its prime factors.
12 = 2 × 2 × 3 18 = 2 × 3 × 3
Step 2: Identify the common and unique prime factors.
Both numbers have 2 and 3 as prime factors. 12 has two 2s, 18 has two 3s.
Step 3: Find the HCF by multiplying the prime factors both numbers share, using the lowest power for each.
The common primes are 2 and 3. The lowest power of 2 is one, and of 3 is one.
HCF = 2 × 3 = 6
Step 4: Find the LCM by multiplying all the prime factors, using the highest power of each found in either number.
The highest power of 2 is two (from 12), and the highest power of 3 is two (from 18).
LCM = 2 × 2 × 3 × 3 = 36
Step 5: State the answers clearly.
The HCF of 12 and 18 is 6. The LCM of 12 and 18 is 36.
