Question 39090: I need some help with a problem where one time I come up with the answer 140 and the other is 240. Can you help me?
How do you find the least common multiple (LCM) for the following group of numbers. 12, 20, and 35. Can you explain how you come up with your answer.
Thanks allot.
Answer by AnlytcPhil(1806) (Show Source):
You can put this solution on YOUR website! I need some help with a problem where one time I come up
with the answer 140 and the other is 240. Can you help me?
How do you find the least common multiple (LCM) for the
following group of numbers. 12, 20, and 35. Can you explain
how you come up with your answer
First prime factor all the numbers
12 = 2·2·3 <--- two 2's and one 3
20 = 2·2·5 <--- two 2's and one 5
35 = 5·7 <--- one 5 and one 7
There are four prime numbers used. These are 2, 3, 5 and 7.
For the factor 2:
The largest number of 2's used in some member of the group is TWO.
So the LCM must contain TWO 2's as factors
So let's write LCM = 2·2·_______
For the factor 3:
The largest number of 3's used in some member of the group is ONE.
So the LCM must contain ONE 3 as a factor
So now we can tack on ONE 3.
Now we have LCM = 2·2·3·_______
For the factor 5:
The largest number of 5's used in some member of the group is ONE.
So the LCM must contain ONE 5 as a factor
So now we can tack on ONE 5.
Now we have LCM = 2·2·3·5_______
For the factor 7:
The largest number of 7's used in some member of the group is ONE.
So the LCM must contain ONE 7 as a factor
So now we can tack on ONE 7.
Now we have LCM = 2·2·3·5·7
That takes care of all factors used, so we are done and
the LCM = 2·2·3·5·7 = 420
Edwin
AnlytcPhil@aol.com
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