Wikipedia Search Least common multiple Article Talk Language Download PDF Watch Edit In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.[1][2] Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.[3] However, some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0. A Venn diagram showing the least common multiples of 2, 3, 4, 5 and 7 (and of their combinations, like 6 and 8). For example, a card game which requires its cards to be divided equally among up to 5 players requires at least 60 cards, the number at the intersection of the 2, 3, 4, and 5 sets, but not the 7 set. The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions. The least common multiple of more than two integers a, b, c, . . . , usually denoted by lcm(a, b, c, . . .), is defined as the smallest positive integer that is divisible by each of a, b, c, . . .[1] Overview Applications Calculation Formulas In commutative rings See also Notes References Last edited 3 months ago by Materialscientist Wikipedia Content is available under CC BY-SA 4.0 unless otherwise noted. Privacy policy Terms of UseDesktop Wikipedia Search Least common multiple Article Talk Language Download PDF Watch Edit In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b.[1][2] Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.[3] However, some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0. A Venn diagram showing the least common multiples of 2, 3, 4, 5 and 7 (and of their combinations, like 6 and 8). For example, a card game which requires its cards to be divided equally among up to 5 players requires at least 60 cards, the number at the intersection of the 2, 3, 4, and 5 sets, but not the 7 set. The least common multiple of the denominators of two fractions is the "lowest common denominator" (lcd), and can be used for adding, subtracting or comparing the fractions. The least common multiple of more than two integers a, b, c, . . . , usually denoted by lcm(a, b, c, . . .), is defined as the smallest positive integer that is divisible by each of a, b, c, . . .[1] Overview Applications Calculation Formulas In commutative rings See also Notes References Last edited 3 months ago by Materialscientist Wikipedia Content is available under CC BY-SA 4.0 unless otherwise noted. Privacy policy Terms of UseDesktop Wikipedia

1. Tuesday, 02 April 2024
HCF and LCM
Starter
Sort the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 into the grid so that they obey the row
and column headings.
Odd Even
Multiple of
3
Prime
Square
Factors of
168
1 4
3
6
5
7
2
9
8

2. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
The highest common factor (HCF)
of two numbers is the highest whole
number which divides into both.
The lowest common multiple (LCM)
of two numbers is the smallest
number that is a multiple of both.

3. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
Example: Find the HCF and the LCM of 12 and 18
Factors of 12:
1 12
2 6
4
3
Factors of 18:
1 18
2 9
6
3
Identify the
common factors
Which is the
highest?
HCF = 6
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120…
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180…
Identify the
common
multiples
Which is the
lowest?
LCM = 36

4. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
Your Turn
Calculate the HCF and LCM of the following pairs of small
numbers by listing factors and multiples.
1. 8 and 10
2. 12 and 15
3. 16 and 24
4. 15 and 18
5. 8 and 12
6. 18 and 24
Challenge: Calculate the HCF and LCM of 12, 15 and 18.

5. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
Answers
Calculate the HCF and LCM of the following pairs of small
numbers by listing factors and multiples.
1. 8 and 10 HCF = 2, LCM = 40
2. 12 and 15 HCF = 3, LCM = 60
3. 16 and 24 HCF = 8, LCM = 48
4. 15 and 18 HCF = 3, LCM = 90
5. 8 and 12 HCF = 4, LCM = 24
6. 18 and 24 HCF = 6, LCM = 72
Challenge: Calculate the HCF and LCM of 12, 15 and 18.
HCF = 3, LCM = 360

6. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
36
3 12
4 3
2 2
36 = 2 × 2 × 3 × 3
= 22 × 32
Prime Factor Trees

7. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
2100
30 70
6
5
2 3
10 7
2 5
2100 = 2 × 2 × 3 × 5 × 5 × 7
= 22 × 3 × 52 × 7
Prime Factor Trees

8. Tuesday, 02 April 2024
HCF and LCM
Express the numbers on the worksheet as products of their prime
factors.
• Reflect – what do you already know?
• Expect – what do you think the answer could be? Why?
• Check – show your working here!
Ask your teacher for the Challenge Task: Each of the numbers have
4 prime factors. Place each of the prime factors in the white boxes
around the larger numbers.

9. Tuesday, 02 April 2024
HCF and LCM
Answers

10. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
Calculate the
HCF and LCM
of 18 and 24.
18
2 9
3 3
24
2 12
2 6
2 3
Factors
of 18
Factors
of 24
2
3
3
2
2
Factors of both
HCF = 2 x 3
= 6
LCM = 3 x 2 x 3 x 2 x 2
= 72

11. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
We can use the factors of a number to find the HCF
and LCM of larger numbers.
Example: Find the HCF and the LCM of 84 and 294
84 294
Think of a common
factor and divide
both numbers by it
42 147
2
Repeat until there are
no common factors
greater than 1
14 49
3
2 7
7
HCF = 2 x 3 x 7 = 42
LCM = 2 x 3 x 7 x 2 x 7 = 588

12. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
We can use the factors of a number to find the HCF
and LCM of larger numbers.
Example: Find the HCF and the LCM of 96 and 72
96 72
Think of a common
factor and divide
both numbers by it
48 36
2
Repeat until there are
no common factors
greater than 1
8 6
6
4 3
2
HCF = 2 x 6 x 2 = 24
LCM = 2 x 6 x 2 x 4 x 3 = 288

13. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
Your Turn
Calculate the HCF and LCM of the following pairs of larger
numbers using the ladder method.
1. 48 and 60
2. 72 and 90
3. 81 and 108
4. 54 and 135
5. 112 and 168
6. 104 and 156
Challenge: Calculate the HCF and LCM of 140, 168 and 196.

14. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
Answers
Calculate the HCF and LCM of the following pairs of larger
numbers using the ladder method.
1. 48 and 60 HCF = 12, LCM = 240
2. 72 and 90 HCF = 18, LCM = 360
3. 81 and 108 HCF = 27, LCM = 324
4. 54 and 135 HCF = 27, LCM = 270
5. 112 and 168 HCF = 56, LCM = 336
6. 104 and 156 HCF = 52, LCM = 312
Challenge: Calculate the HCF and LCM of 140, 168 and 196.
HCF = 28, LCM = 5880

15. Tuesday, 02 April 2024
HCF and LCM

16. Tuesday, 02 April 2024
HCF and LCM
Keywords
Factor, prime number, tree, product, multiple, common, highest, lowest
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53…
Lesson
Objectives:
Developing
students will be
able to write
numbers as
products of their
prime factors.
Secure students
will be able to
calculate the HCF
and LCM of pairs
of numbers using
Venn diagrams.
Excelling students
will be able to
answer worded
questions on HCF
and LCM.
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2 things you
learnt today
1 question about
today’s topic