EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: HCF and LCM
HCF and LCM · Number · Lesson 3 of 7 · 12 marks · 25 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
Write 180 as a product of its prime factors. Give your answer in index form.
Question 2 NON-CALCULATOR [2 marks]
A = 2³ × 3 × 5² and B = 2² × 3³ × 7. (a) Find the highest common factor of A and B. (b) Find the lowest common multiple of A and B. You may leave your answers in index form.
Question 3 NON-CALCULATOR [3 marks]
Light A flashes every 20 seconds. Light B flashes every 45 seconds. Both lights flash at 10 pm. At what time will they next flash together?
Question 4 NON-CALCULATOR [3 marks]
Paper cups are sold in packs of 24. Paper plates are sold in packs of 36. Amir wants to buy exactly the same number of cups and plates. What is the smallest number of packs of cups and the smallest number of packs of plates he can buy?
Question 5 NON-CALCULATOR [2 marks]
The HCF of two numbers is 6. The LCM of the same two numbers is 36. Both numbers are greater than 6. Find the two numbers.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
180 = 2² × 3² × 5
▸ A correct method, e.g. a factor tree with at least two correct steps, or 2, 2, 3, 3, 5 seen M1
▸ 2² × 3² × 5 A1
Question 2 [2 marks]
(a) HCF = 2² × 3 = 12 (b) LCM = 2³ × 3³ × 5² × 7 = 37 800
▸ (a) 2² × 3 or 12 B1
▸ (b) 2³ × 3³ × 5² × 7 or 37 800 B1
Question 3 [3 marks]
20 = 2² × 5 and 45 = 3² × 5, so the LCM is 2² × 3² × 5 = 180 seconds = 3 minutes. They next flash together at 10:03 pm.
▸ Lists multiples of 20 and 45, or writes both as products of primes P1
▸ 180 (seconds) or 3 minutes P1
▸ 10:03 pm A1
Question 4 [3 marks]
24 = 2³ × 3 and 36 = 2² × 3², so the LCM is 2³ × 3² = 72. 72 ÷ 24 = 3 packs of cups and 72 ÷ 36 = 2 packs of plates.
▸ Lists multiples of 24 and 36, or writes both as products of primes P1
▸ 72 P1
▸ 3 packs of cups and 2 packs of plates A1
Question 5 [2 marks]
Both numbers are multiples of 6 and factors of 36, so they come from 12 and 18 (6 and 36 are ruled out). HCF(12, 18) = 6 and LCM(12, 18) = 36. The numbers are 12 and 18.
▸ Considers multiples of 6 that are factors of 36, e.g. 12, 18 seen P1
▸ 12 and 18 A1