Question 203417
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.<br>
How does one find the LCM when it is not multiple choice? There are a variety of ways. One way is to<ol><li>factor each number/term fully (i.e. prime factorization on numbers)</li><li>the LCM is the product of all the different factors. When there is a common factor, use the factor with its highest exponent.</li></ol>
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<br>
LCM of 12, 18 and 30
{{{12 = 2^2*3}}}
{{{18 = 2*3^2}}}
{{{30 = 2*3*5}}}
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.
{{{LCM = 2^2*3^2*5 = 180}}}