REVIEWING HCF AND LCM

ONLY FOR 3 OR 4 NUMBERS!

FOR 2 NUMBERS..•NOTHING CHANGES!•DRAW THE VENN DIAGRAM! •HCF WHAT IS COMMON (IN THE MIDDLE)•LCM WHAT IS IN THE MIDDLE X WHAT IS LEFT IN THE OTHER TWO CIRCLES

223

2

Highest Common Factor (HCF)

24 60

5

If we multiply all the numbers in the intersection,

we can quickly find the Highest Common Factor (HCF) = 2 x 2 x 3 = 12

223

2

Lowest Common Multiple (LCM)

24 60

5

If we multiply all the numbers in Venn Diagram, we get the Lowest Common

Multiple (LCM) = 2 x 2 x 2 x 3 x 5 =

120

FOR 3 OR 4 NUMBERS…• HCF – WE ALWAYS FIND WHAT IS

COMMON (NOTHING CHANGES!)•TO FIND THE LCM – THE METHOD WAS GIVING US A COMMON MULTIPLE , BUT NOT THE LOWEST COMMON MULTIPLE!

WHY?

THE VENN DIAGRAM FOR 3 OR 4 NUMBERS

10

15

20

10 5,2 15 5 , 3

20 5, 2, 2 5

What is common FOR

10,15 AND 20?

What is common FOR 10 AND 15?

5 ONLY

What is common FOR 15 AND 20 ? 5 ONLY

What is common FOR 10 AND

20 ?

2

What is LEFT?

3

2HCF =

5LCM = 5 x 3 x 2 x 2 = 60!

No. 22

SHORTCUT: MULTIPLY THE HIGHEST POWERS OF EACH FACTOR!!

SHORTCUT TO FIND LCM (WITHOUT DRAWING VENN DIAGRAM)

10 5,2

15 5 , 3

20 5, 2, 2

10 5 x 2

PRIME FACTORS IN INDEX FORM

15 5 x 3

20 5 x 22

5 x 3 x 22

The HIGHEST power of EACH factor

(of 5, of 3 and of 2)

LCM = 5 x 3 x 22 = 60!!

THESE RULES ALSO APPLY WHEN WE HAVE 3 OR 4 NUMBERS!

BOOK PG 53 EXERCISE 4J NUMBER 6: 21,42,84

7 3 7 6

3

7 12

34

2 2

7, 3 2

21

42

84

7, 3, 2

7, 2, 2, 3

What’s common?7 and 3

HCF = 7 x 3 = 21

Times the Highest Powers of each

factor (7, 3 and 2) to find the LCM

LCM = 7 x 3 x 22 = 84

7 x 3

7 x 3 x 2

7 x 22 x 3

THESE RULES ALSO APPLY WHEN WE HAVE 3 OR 4 NUMBERS!

BOOK PG 53 EXERCISE 4J NUMBER 10: 39,13,26

3 13 2 1

3

3, 13

39

13

26

13 2, 13

What’s common?13HCF = 13 Prime

numbers don’t have

prime factors, they are prime!

Times the highest powers of each factor (2,3,13)

LCM = 2 x 3 x 13 = 78

3 x 13

13 2 x 13

NUMBER 12: 10,18,20,3610

5 2

5, 2

18

9 2

3 33 , 3 ,

2

20

2 10

5 22 , 5 ,

2

36

6 6

2 3 2 32 , 3 , 2 ,

3

What’s common?2

HCF = 2

Times the highest powers of each factor (5,2,3)LCM =5 x 22 x

32=180

5 x 2 32 x 2 22 x 5 22 x 32

NUMBER 11: 15,30,45,60

15

5

3, 5

30

2

3

3

5, 3, 2

45

5, 3, 3

60

3

5 , 3 , 2 , 2

15

5

15 3

5 3

15 4

5 2 2

What’s common?3 and 5

HCF = 5 x 3 = 15

Times the highest powers of each factor (5,2,3)LCM =5 x 22 x

32=180

3 x 5 5 x 3 x 2 5 x 32 5 x 3 x

22

NUMBER 20: 18,27,3618

2

3, 3, 2

27

9

3

9

3, 3, 3

36

3, 3, 2, 2

What’s common?3 and 3

HCF = 3 x 3 = 9

33 3

3 9 4

3 3 2 2

Times the highest powers of each

factor (2,3)LCM = 33 x 22 = 108

32 x 2 33 32 x 22

10 5,2

15 5 , 3

20 5, 2, 2

10 5 x 2

PRIME FACTORS IN INDEX FORM

15 5 x 3

20 5 x 22

5 x 3 x 22

The HIGHEST power of EACH factor

(of 5, of 3 and of 2)

LCM = 5 x 3 x 22 = 60!!

No. 22