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Learning Objective:
• N4 use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common
factors, common multiples, highest common factor, lowest common multiple, prime
factorisation, including using product notation and the unique factorisation theorem
Worked Example 1
What are the Multiples of 7
Worked Example 2
What are the factors of 24
HCF and LCM
Write down the numbers in the 7 times table:
Answer = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77 ……..
Step 1 – List the values that multiply together that gives you 24
1 x 24
2 x 12
3 x 8
4 x 6
Step 2 – The factors of 24 are:
Answer = 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Write 102 as a product of its prime factors
Answer = _______________
Worked Example 4
A number is expressed as a product of its prime factors as: 23 × 32 × 5
What is the number?
Answer = __________________
360
HCF and LCM
Worked Example 5
Find the Lowest Common Multiple of the numbers below
4 and 6
Answer = ________________
Worked Example 6
Find the Lowest Common Multiple of the numbers below
36 and 54
Answer = __________________
HCF and LCM
Step 1 – Workout the LCM using the inverse cake method
Step 2 – Work out the LCM
Step 1 – Workout the LCM using the inverse cake method
Step 2 – Work out the LCM
Worked Example 7a
Find the Highest Common Factor of the numbers below using the upside-down cake method
12 and 24
Answer = ________________
Step 1 – Workout the HCF using the inverse cake method
Step 2 – Work out the HCF
HCF and LCM
Worked Example 7b
Find the Highest Common Factor of the numbers by using the prime factor method.
12 and 24
Answer = _________________
Step 1 – Find the prime factors of 12 and 24 by drawing a factor tree
Step 2 – Write 12 and 24 as product of prime factor
Step 3 – Multiply the numbers that appear as a product of prime factor for both 12
and 24 once to find the HCF
HCF and LCM
Worked Example 8
Find the LCM and HCF of the numbers below
18, 30, and 21
HCF = ____________________
LCM = _____________________
Step 1 – Workout the LCM and HCF using the inverse cake method
Step 2 – Work out the HCF
Step 3 – Work out the LCM
HCF and LCM
Practice Questions
Question 1
What is the highest common factor of 24 and 30?
Answer = __________________________
Question 2
What is the lowest common multiple of 24 and 48?
Answer = __________________________
Question 3
What is the lowest common multiple of 12 and 15?
Answer = _________________________
HCF and LCM
Question 4
What is the highest common factor of 90 and 165?
Answer = __________________________
Question 5
What is the HCF and LCM of 390 and 160
LCM = _________________________
HCF = _________________________
HCF and LCM
Question 6
Below is an incomplete factor tree. Fill in the gaps below
25
100
HCF and LCM
Question 7
Below is an incomplete factor tree. Fill in the gaps below
Question 8
Ravi is organising a party. He has 24 party-poppers and 18 balloons, and wants to know the largest
number of tables needed so that each table has the same number of balloons on it, and that the
party-poopers are also evenly distributed.
Answer = __________________________
66
HCF and LCM
Question 9
Dixie is making up first-aid kits. She has 32 plasters, 24 cleaning wipes and 16 wound dressing. Each
first aid must be identical, and must allocate everything. How many first-aid kits can she make?
Answer = __________________________
Question 10
Express 200 as a product of powers of its prime factors
Answer = __________________________
HCF and LCM
Question 11
Find the Highest Common Factor and Lowest Common Multiple of 75 and 90
LCM = _________________________
HCF = _________________________
Question 12
Express 300 as a product of its prime factors
Answer = ____________________
HCF and LCM
Question 13
Find the Highest Common Factor and Lowest Common Multiple of 54 and 90
LCM = _________________________
HCF = _________________________
Question 14
Express 204 as a product of its prime factors
Answer = __________________
HCF and LCM
Question 15
A = 23 x 32 x 54
B = 35 x 5 x 73
Find the Highest Common Factor (HCF) of A and B
Answer = __________________
Question 16
Express 600 as a product of its prime factors
Answer = __________________
HCF and LCM
Question 17
a..) Write 252 as a product of its prime factors
Answer = _________________
b..) Given that 240 = 24 x 3 x 5
And that y = 240 x 252
Write y as a product of powers of its prime factors
Answer = _________________
Question 18
x is an integer The LCM of x and 12 and is 120 The HCF of x and 12 is 4 Work out the value of x
Answer = ______________
HCF and LCM
Question 19
The highest common multiple (HCF) of 140 and x is 20
The lowest common multiple (LCM) of 140 and x is 420
Find the value of x
Answer = _________________
Question 20
Find the HCF of the 4 number below
14,15,21,28
Answer = __________________
HCF and LCM
Question 21
Find the LCM of the 4 number below
12,15,21,28
Answer = __________________
HCF and LCM
