The least
common multiple (LCM) of two numbers is the smallest number (not
zero) that is a multiple of both.
*Review: A
multiple
is found by multiplying the given number by 1, by 2, by 3, and so on.*
We can find the
LCM of two or more
numbers by looking at their prime factors. Use factor trees
to find the prime factors. |
Take a look at this example...
What is the LCM of 16 and 20?
The prime factors of 16 are 2
· 2 · 2 · 2
AND
The prime factors of 20 are 2 · 2 · 5
We now
multiply each factor the greatest number of times it occurs in
either number. |
2 occurs four times in the 16
AND
1 occurs once in the 20
SO...
We multiply 2
· 2 · 2 · 2 · 5 and find
the LCM to be 80. |
What if we had three numbers?
What is the LCM of 6, 9, and 12?
The prime factors of 6 are 2
· 3,
The prime
factors of 9 are 3 · 3,
AND
The prime factors of 12 are 2 · 2 · 3 |
2 occurs two times in the 12
AND
3 occurs two times in the 9
SO...
We multiply 2
· 2 · 3 · 3 and find
the LCM to be 36. |
Let's
Practice
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