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Find the least common multiple of 14, 21, and 35.
\n" ); document.write( "A. 70
\n" ); document.write( "70 is a multiple of 35 and 14 but not a multiple of 21
\n" ); document.write( "B. 10,290
\n" ); document.write( "20,290 is a multiple of all three numbers, but it is not the LCM.
\n" ); document.write( "C. 42
\n" ); document.write( "42 is a multiple of 14 and 21 but not a multiple of 35
\n" ); document.write( "D. 210
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "Here are some examples:
\n" ); document.write( "LCM of 14, 21, 35
\n" ); document.write( "14 = 2*7
\n" ); document.write( "21 = 3*7
\n" ); document.write( "35 = 5*7
\n" ); document.write( "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
\n" ); document.write( "LCM = 2*3*5*7 = 210
\n" ); document.write( "LCM of 12, 18 and 30
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\n" ); document.write( "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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