Least Common Multiple Notes

```Least Common Multiple Notes
Common Multiples (page 52 in book)
To find common multiples of a set of numbers, do “count-bys” and find numbers (multiples) that
are in the lists of all of the numbers in your set.
For example, to find the common multiples of 4,3, and 6 make lists as follows:
4 - 4, 8, 12, 16, 20, 24, 28, 32, 36
3 - 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
6 - 6, 12, 18, 24, 30, 36, 42, 48, 54
Since 12 and 24 and 36 are in all three lists, these are common multiples of these numbers.
Least Common Multiple (page 52 in book)
This is basically the same as common multiple, but you need to find the lowest number that is in all
of the lists of multiples
For example, to find the least common multiple of 4,3, and 6 make lists as follows:
4 - 4, 8, 12, 16, 20, 24, 28, 32, 36
3 - 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36
6 - 6, 12, 18, 24, 30, 36, 42, 48, 54
Since 12 is the lowest number in all three lists, this is the least common multiple of these
numbers.
To find the Common Multiples without making the whole list:
Make lists long enough to find the first common multiple.
Once you find it - double it. That’s the next common multiple.
To find the third one, calculate how far apart the first two multiples are. That will be your
“jump” to the next common multiples.
Common Factors (page 108 in book)
To find common factors of sets of numbers, you must first find all of the factors of each number.
Begin by writing each number on a separate line with 1 at the beginning of the line and the numbers
themselves at the end of the line. Then fill in the factors in pairs working from both ends of the line.
For example, to find the common factors of 20 and 48, follow these steps:
1
20
1 2
10
20
1 2
4
5
10
20
These are all of the factors of 20
1
1
1
1
1
2
2
2
2
3
3
4
12
3
4
6
8
12
These are all of the factors of 48
16
16
16
24
24
24
24
48
48
48
48
48
Since 2 and 4 are in both lists, these are the common factors of 20 and 48.
Greatest Common Factor (page 108 in book)
This is basically the same as common factors, but you need to find the greatest number that is in
all of the lists of factors
For example, to find the greatest common factor of 20 and 48 make lists as you did above and
find the greatest number in both lists. 4 would be the greatest common factor.
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