Is 84 a multiple of 6? Write yes or no and show a check.
(1)
3
Write 20 as a product of its prime factors.
(1)
4
Find the LCM of 5 and 8 by listing multiples of each.
(1)
5
Find the highest common factor (HCF) of 20 and 30 by listing the factors of each number.
(2)
6
Use prime factorisation to find the HCF of 24 and 36.
(2)
7
Use prime factorisation to find the LCM of 6 and 14.
(2)
8
Is 17 a prime number? Explain your answer by checking for factors.
(2)
9
Find the two whole numbers strictly between 50 and 100 that are multiples of both 4 and 5.
(2)
10
List the first three common multiples of 3 and 4.
(2)
11
Find the HCF of 42 and 56.
(2)
12
Write 50 as a product of its prime factors.
(1)
13
Find the LCM of 9 and 12 by listing multiples of each.
(1)
14
Is this statement true or false? "Every multiple of 8 is also a multiple of 4." Give a reason for your answer.
(2)
15
A chess club meets every 8 days and an art club meets every 10 days. Both clubs meet today. In how many days will both clubs next meet on the same day? Show your working.
(3)
16
A baker has 60 cupcakes and 84 cookies. She wants to pack them into identical boxes so that each box has the same number of cupcakes and the same number of cookies, with none left over. What is the greatest number of boxes she can pack? Show your working.
(3)
17
Three delivery vans leave a warehouse together. Van A leaves every 12 minutes, Van B every 18 minutes and Van C every 24 minutes. If all three leave together at 09:00, after how many minutes will they next all leave together? Show your working.
(3)
18
Two numbers have HCF 8 and LCM 96. One of the numbers is 24. Find the other number. Show your working.
(3)
19
Explain why the sum of two multiples of 5 is always a multiple of 5. Use algebra in your explanation.
(3)
20
A gardener waters flower bed A every 15 days and flower bed B every 20 days. She waters both beds today. Over the next 100 days (not counting today), how many more times will she water both beds on the same day? Show your working.
(3)
Mark scheme · KS3.M-N6D Factors, Multiples, HCF and LCM: Fluency and Exam Drill
Question 1
B1 1, 2, 3, 4, 6, 8, 12, 24 all correct
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Question 2
B1 yes, since 84 = 6 x 14 (or equivalent check)
Answer: Yes
Question 3
B1 22 x 5 cao
Answer: 22 x 5
Question 4
B1 40 cao
Answer: 40
Question 5
M1 correct factor list for 20 and for 30 (or equivalent method) shown
A1 10 cao
Answer: 10
Question 6
M1 correct prime factorisations 24 = 23 x 3 and 36 = 22 x 32 (or equivalent method)
A1 12 cao
Answer: 12
Question 7
M1 correct prime factorisations 6 = 2 x 3 and 14 = 2 x 7 (or equivalent method)
A1 42 cao
Answer: 42
Question 8
B1 correct conclusion that 17 is prime
B1 valid reason, e.g. 17 is not divisible by 2 or 3, and no need to check beyond √17
Answer: Yes, 17 is prime
Question 9
M1 recognises LCM(4,5) = 20 (or lists multiples of both 4 and 5)
A1 60 and 80 cao
Answer: 60 and 80
Question 10
M1 recognises LCM(3,4) = 12 (or lists multiples of both)
A1 12, 24, 36 cao
Answer: 12, 24, 36
Question 11
M1 correct prime factorisations 42 = 2 x 3 x 7 and 56 = 23 x 7 (or equivalent method)
A1 14 cao
Answer: 14
Question 12
B1 2 x 52 cao
Answer: 2 x 52
Question 13
B1 36 cao
Answer: 36
Question 14
B1 correct answer, true
B1 valid reason, e.g. 8 = 4 x 2, so any multiple of 8 is 4 x (2 x k), which is a multiple of 4
Answer: True
Question 15
M1 correct prime factorisations 8 = 23 and 10 = 2 x 5 (or equivalent method)
M1 correctly combines to LCM = 23 x 5
A1 40 cao
Answer: 40 days
Question 16
M1 correct prime factorisations 60 = 22 x 3 x 5 and 84 = 22 x 3 x 7 (or equivalent method)
M1 correctly combines to HCF = 22 x 3
A1 12 cao
Answer: 12 boxes
Question 17
M1 correct prime factorisations 12 = 22 x 3, 18 = 2 x 32 and 24 = 23 x 3 (or equivalent method)
M1 correctly combines to LCM = 23 x 32
A1 72 cao
Answer: 72 minutes
Question 18
M1 uses HCF x LCM = product of the two numbers, 8 x 96 = 768
M1 divides by the known number, 768 / 24
A1 32 cao
Answer: 32
Question 19
M1 writes the two multiples as 5m and 5n for integers m, n
M1 correctly sums to 5m + 5n = 5(m + n)
A1 correct conclusion that 5(m+n) is a multiple of 5 since m+n is an integer
Answer: 5m + 5n = 5(m + n), which is a multiple of 5, so the sum of two multiples of 5 is always a multiple of 5.
Question 20
M1 correct prime factorisations 15 = 3 x 5 and 20 = 22 x 5 (or equivalent method)
M1 correctly combines to LCM = 60, and identifies multiples of 60 up to 100 (only 60)