The Least Common Multiple
(LCM) is the smallest number that two or more numbers will divide
into evenly.
To find the multiples of
a number simply multiply the number by every whole number.
For example, to find the multiples of 4 we follow this pattern
0 (4x0), 4
(4x1), 8 (4x2),
12 (4x3), 16 (4x4) ...
To find the multiples of 8:
0 (8x0), 8
(8x1), 16 (8x2),
24 (8x3) 32 (8x4)...
When we are asked for a set of multiples we just list them like
this.
M_{7} = 0,7, 17, 21, 28, 35, 42, 49, ... 
Let's start with
an easy example.
Let's look at the set of multiples for the two numbers 4 and 6
M_{4} = 0, 4, 8,
12, 16, 20,
24, 28, 32, 36, 40 ...
M_{6} = 0, 6,
12, 18, 24,
30, 36, 42 ...

Did you notice
that 0, 12, 24 and 36 were in both lists?
We call these common multiples.
The smallest
nonzero common multiple is called the "Least Common Multiple"
So the LCM for 4
and 6 is
12.
Let's look at
another example.
Find the LCM for 12 and 16
First list the multiples of both numbers.
M_{12} = 0, 12, 24, 36, 48,
60, 72, 84, 96 ...
M_{16
}= 0, 16, 32, 48, 64, 80, 96
...
The smallest nonzero common multiple is
48.
Therefore the LCM for 12 and 16 is 48.

The number of
multiples in your list depends on the number being used. The LCM is
usually within the first 10 multiples. If it doesn't appear by then
just keep adding multiples until one appears on both lists.
Now,
let's get serious!
Find the LCM for 9, 12 and 36
M_{9
}=_{ }0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 ..._{
}M_{12 }=_{
}M_{36 }=

During the month Sheila put
money into her account and took money out. You have to figure
how much money she had at the beginning of the month
To do that, start with the
ending balance and work backwards, using inverse
operations.
Start with ending balance
Add
back $14 check charge
Add back $617 check
Add back $98 check
Subtract $385 deposit

$899
+ 14
913
+617
1530
+ 98
1628
385
$1249
balance at end of May

