HCF & LCM

Read the formula sheet first, then work through the 15 questions below. Each answer comes with a step-by-step solution — read it even when you get the question right, the shortcut is often faster than your method.

Formula sheet

• HCF = product of lowest powers of common prime factors; LCM = product of highest powers of all primes.
• Product of two numbers = HCF × LCM.
• HCF of fractions = HCF(numerators) / LCM(denominators); LCM of fractions = LCM(numerators) / HCF(denominators).
• Greatest number that divides a, b, c leaving remainders r₁, r₂, r₃ → HCF of (a−r₁), (b−r₂), (c−r₃).
• Least number that leaves the same remainder r on dividing by a, b, c → LCM(a,b,c) + r.
• Least number that is divisible by a, b, c → LCM; if leaves remainder k less than each divisor → LCM − k.
• Bells / traffic lights / runners meeting again → LCM of the time gaps.

Practice

Pick an answer to see whether it is right and the worked solution. Your score is saved when you finish the set.