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Question 203417: Find the least common multiple of 14, 21, and 35.
A. 70
B. 10,290
C. 42
D. 210
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Find the least common multiple of 14, 21, and 35.
A. 70
70 is a multiple of 35 and 14 but not a multiple of 21
B. 10,290
20,290 is a multiple of all three numbers, but it is not the LCM.
C. 42
42 is a multiple of 14 and 21 but not a multiple of 35
D. 210
This is a multiple of all three and it is lower than 10,290. So unless the problem does not include the right answer, this must be it.
How does one find the LCM when it is not multiple choice? There are a variety of ways. One way is to- factor each number/term fully (i.e. prime factorization on numbers)
- the LCM is the product of all the different factors. When there is a common factor, use the factor with its highest exponent.
Here are some examples:
LCM of 14, 21, 35
14 = 2*7
21 = 3*7
35 = 5*7
The different factors are 2, 3, 5 and 7. Since 7 is common, we will only use it once, with its highest exponent (which happens to be 1). Therefore
LCM = 2*3*5*7 = 210
LCM of 12, 18 and 30
The different factors are: 2, 3 and 5. 2 and 3 occur in more than one of the numbers. We will use the highest exponent on each: 2^2, 3^2.
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