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FINDING LEAST COMMON MULTIPLES
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See the best ALGEBRA PINBALL time for this exercise
The concepts for this exercise are summarized below.
For a complete discussion, read the text.
The multiples of 2 and 3 are:
multiples of 2 : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, etc.
multiples of 3 : 3, 6, 9, 12, 15, 18, 21, 24, etc.
What numbers are multiples of both 2 and 3 ?
That is, what numbers appear in both lists above?
Answer: 6, 12, 18, etc.
What is the least number that is a multiple of both 2 and 3 ?
Answer: 6
The number 6 is called the least common multiple of 2 and 3 ,
because it is a common multiple (i.e., it is a multiple of 2 and a multiple of 3 ),
and it is the smallest number with this property.
FINDING A LEAST COMMON MULTIPLE
If the individual numbers aren't too big,
then the quickest way to come up with the least common multiple
is to mentally go through the multiples of the largest number,
checking each to see if it is a multiple of all the numbers.
For example, suppose that you want the least common multiple of 3, 5, and 20.
Go through the multiples of 20 , stopping to check if each is divisible by the other two numbers,
3 and 5 .
Is 20 divisible by both 3 and 5 ? No; it's not divisible by 3 .
Is 40 divisible by both 3 and 5 ? No; it's not divisible by 3 .
Is 60 divisible by both 3 and 5 ? Yes! So, 60 is the least common multiple.
EXAMPLES:
The least common multiple of 2 and 3 is 6.
The least common multiple of 4 and 12 is 12.
The least common multiple of 6 and 15 is 30.