Math Olympiad 3

Week	Topic and action
Week 49	Multiples & LCM Practice Evaluation

Multiples & LCM

The multiples of a whole number are found by taking the product of any counting number and that whole number.
Below are some examples of multiples. For example, to find the multiples of 3, multiply 3 by 1, 3 by 2, 3 by 3, and so on.

Multiplication 1 × 2 2 × 2 3 × 2 4 × 2 5 × 2 6 × 2 7 × 2 8 × 2 9 × 2 10 × 2
Multiples of 2 2 4 6 8 10 12 14 16 18 20
Multiplication 1 × 3 2 × 3 3 × 3 4 × 3 5 × 3 6 × 3 7 × 3 8 × 3 9 × 3 10 × 3
Multiples of 3 3 6 9 12 15 18 21 24 27 30
Multiplication 1 × 4 2 × 4 3 × 4 4 × 4 5 × 4 6 × 4 7 × 4 8 × 4 9 × 4 10 × 4
Multiples of 4 4 8 12 16 20 24 28 32 36 40
Multiplication 1 × 5 2 × 5 3 × 5 4 × 5 5 × 5 6 × 5 7 × 5 8 × 5 9 × 5 10 × 5
Multiples of 5 5 10 15 20 25 30 35 40 45 50
Multiplication 1 × 6 2 × 6 3 × 6 4 × 6 5 × 6 6 × 6 7 × 6 8 × 6 9 × 6 10 × 6
Multiples of 6 6 12 18 24 30 36 42 48 54 60
Multiplication 1 × 7 2 × 7 3 × 7 4 × 7 5 × 7 6 × 7 7 × 7 8 × 7 9 × 7 10 × 7
Multiples of 7 7 14 21 28 35 42 49 56 63 70
Multiplication 1 × 8 2 × 8 3 × 8 4 × 8 5 × 8 6 × 8 7 × 8 8 × 8 9 × 8 10 × 8
Multiples of 8 8 16 24 32 40 48 56 64 72 80
Multiplication 1 × 9 2 × 9 3 × 9 4 × 9 5 × 9 6 × 9 7 × 9 8 × 9 9 × 9 10 × 9
Multiples of 9 9 18 27 36 45 54 63 72 81 90
Common multiples: Multiples that are common to the whole numbers. For example,
- Some common multiples of 2 and 3 are:6, 12, 18, 24, 30 ...
- Some common multiples of 3 and 4 are:12, 24, 36, 48, 60 ...
- Some common multiples of 2, 4 and 5 are:20, 40, 60, 80, 100 ...
- Some common multiples of 3, 4 and 5 are:60, 120, 180, 240, 300 ...
Least Common multiple: The Least Common Multiple of a set of whole numbers is the smallest multiple common to all whole numbers in the set.
- Make a list of multiples for each whole number.
- Continue your list until at least two multiples are common to all lists.
- Identify the common multiples.
- The Least Common Multiple (LCM) is the smallest of these common multiples.
For example,
- Least common multiple of 2 and 3 is:6
- Least common multiple of 3 and 9 is:9
- Least common multiple of 4 and 9 is:36
- Least common multiple of 5 and 8 is:40
- Least common multiple of 6 and 9 is:18
- Least common multiple of 7 and 8 is:56
- Least common multiple of 8 and 9 is:72
- Least common multiple of 2, 4 and 6 is:12
- Least common multiple of 3, 4 and 5 is:60
- Least common multiple of 4, 6 and 8 is:24

Multiplication	1 × 2	2 × 2	3 × 2	4 × 2	5 × 2	6 × 2	7 × 2	8 × 2	9 × 2	10 × 2
Multiples of 2	2	4	6	8	10	12	14	16	18	20

Multiplication	1 × 3	2 × 3	3 × 3	4 × 3	5 × 3	6 × 3	7 × 3	8 × 3	9 × 3	10 × 3
Multiples of 3	3	6	9	12	15	18	21	24	27	30

Multiplication	1 × 4	2 × 4	3 × 4	4 × 4	5 × 4	6 × 4	7 × 4	8 × 4	9 × 4	10 × 4
Multiples of 4	4	8	12	16	20	24	28	32	36	40

Multiplication	1 × 5	2 × 5	3 × 5	4 × 5	5 × 5	6 × 5	7 × 5	8 × 5	9 × 5	10 × 5
Multiples of 5	5	10	15	20	25	30	35	40	45	50

Multiplication	1 × 6	2 × 6	3 × 6	4 × 6	5 × 6	6 × 6	7 × 6	8 × 6	9 × 6	10 × 6
Multiples of 6	6	12	18	24	30	36	42	48	54	60

Multiplication	1 × 7	2 × 7	3 × 7	4 × 7	5 × 7	6 × 7	7 × 7	8 × 7	9 × 7	10 × 7
Multiples of 7	7	14	21	28	35	42	49	56	63	70

Multiplication	1 × 8	2 × 8	3 × 8	4 × 8	5 × 8	6 × 8	7 × 8	8 × 8	9 × 8	10 × 8
Multiples of 8	8	16	24	32	40	48	56	64	72	80

Multiplication	1 × 9	2 × 9	3 × 9	4 × 9	5 × 9	6 × 9	7 × 9	8 × 9	9 × 9	10 × 9
Multiples of 9	9	18	27	36	45	54	63	72	81	90

Relationship between least common multiple (LCM) and greatest common factor(GCF) of two whole numbers.

Multiplication	GCF	LCM	GCF×LCM
2 × 5 = 10	1	10	1 × 10 = 10
3 × 9 = 27	3	9	3 × 9 = 27
4 × 9 = 36	1	36	1 × 36 = 36
5 × 8 = 40	1	40	1 × 40 = 40
6 × 8 = 48	2	24	2 × 24 = 48
7 × 8 = 56	1	56	1 × 56 = 56
8 × 9 = 72	1	72	1 × 72 = 72

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